Solve the quadratic equation 3x2 + 7x − 15 = 0.

Question

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To solve the quadratic equation 3x² + 7x − 15 = 0, I will use the quadratic formula. Step 1: Identify the coefficients a, b, and c. For the equation ax² + bx + c = 0: a = 3; b = 7; c = −15; Step 2: Apply the quadratic formula, x = (−b ± √(b² − 4ac))/(2a). x = (−(7) ± √((7)² − 4(3)(−15)))/(2(3)) Step 3: Calculate the value under the square root (the discriminant). b² − 4ac = (7)² − 4(3)(−15); = 49 − (−180); = 49 + 180; = 229 Step 4: Substitute the discriminant back into the quadratic formula and simplify. x = (−7 ± √(229))/(6) Step 5: Write out the two possible solutions for x. x₁ = (−7 + √(229))/(6); x₂ = (−7 − √(229))/(6) The solutions for the equation are: x = (−7 ± √(229))/(6)

Solve the quadratic equation 3x2 + 7x − 15 = 0.

Answer

Step-by-step solution

Identify the coefficients $a$ , $b$ , and $c$ .

Apply the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

Calculate the value under the square root (the discriminant).

Substitute the discriminant back into the quadratic formula and simplify.

Write out the two possible solutions for $x$ .

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Solve the quadratic equation 3x2 + 7x − 15 = 0.

Answer

Step-by-step solution

Identify the coefficients aaa, bbb, and ccc.

Apply the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​.

Calculate the value under the square root (the discriminant).

Substitute the discriminant back into the quadratic formula and simplify.

Write out the two possible solutions for xxx.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Identify the coefficients $a$ , $b$ , and $c$ .

Apply the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

Write out the two possible solutions for $x$ .