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Simplifying 4x2 + 32x + -15 = 0 Reorder the terms: -15 + 32x + 4x2 = 0 Solving -15 + 32x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 8x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 8x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 8x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 8x + x2 = 0 + 3.75 8x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 8x + x2 = 3.75 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 3.75 + 16 Reorder the terms: 16 + 8x + x2 = 3.75 + 16 Combine like terms: 3.75 + 16 = 19.75 16 + 8x + x2 = 19.75 Factor a perfect square on the left side: (x + 4)(x + 4) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + 4) equal to 4.444097209 and -4.444097209.Subproblem 1
x + 4 = 4.444097209 Simplifying x + 4 = 4.444097209 Reorder the terms: 4 + x = 4.444097209 Solving 4 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.444097209 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.444097209 + -4 x = 4.444097209 + -4 Combine like terms: 4.444097209 + -4 = 0.444097209 x = 0.444097209 Simplifying x = 0.444097209Subproblem 2
x + 4 = -4.444097209 Simplifying x + 4 = -4.444097209 Reorder the terms: 4 + x = -4.444097209 Solving 4 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.444097209 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.444097209 + -4 x = -4.444097209 + -4 Combine like terms: -4.444097209 + -4 = -8.444097209 x = -8.444097209 Simplifying x = -8.444097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.444097209, -8.444097209}
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