Solve 5y2 + 8y − 100 = y2 + 4y − 37

Question

ScanSolve AI Tutor · Accepted Answer

Here is the solution to the equation: 20) Solve 5y² + 8y − 100 = y² + 4y − 37 Step 1: Move all terms to one side of the equation to set it equal to zero. 5y² − y² + 8y − 4y − 100 + 37 = 0 Step 2: Combine like terms. 4y² + 4y − 63 = 0; Step 3: Use the quadratic formula y = (−b ± √(b² − 4ac))/(2a) to solve for y. Here, a=4, b=4, and c=−63. y = (−4 ± √(4² − 4(4)(−63)))/(2(4)); y = (−4 ± √(16 + 1008))/(8); y = (−4 ± √(1024))/(8) Step 4: Calculate the square root. √(1024) = 32 Step 5: Substitute the value back into the formula and find the two possible solutions for y. y = (−4 ± 32)/(8) For the first solution: y₁ = (−4 + 32)/(8) = 28/8 = 7/2 For the second solution: y₂ = (−4 − 32)/(8) = (−36)/(8) = −9/2 The solutions are: y = 7/2, y = −9/2

Solve 5y2 + 8y - 100 = y2 + 4y - 37

Answer

Step-by-step solution

Move all terms to one side of the equation to set it equal to zero.

Combine like terms.

Use the quadratic formula $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ to solve for $y$ .

Calculate the square root.

Substitute the value back into the formula and find the two possible solutions for $y$ .

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