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Simplifying 0 = 4x2 + 4x + -87 Reorder the terms: 0 = -87 + 4x + 4x2 Solving 0 = -87 + 4x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 87 = 87 87 + -4x + -4x2 = -87 + 4x + 4x2 + 87 + -4x + -4x2 Reorder the terms: 87 + -4x + -4x2 = -87 + 87 + 4x + -4x + 4x2 + -4x2 Combine like terms: -87 + 87 = 0 87 + -4x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2 87 + -4x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 87 + -4x + -4x2 = 0 + 4x2 + -4x2 87 + -4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 87 + -4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -21.75 + x + x2 = 0 Move the constant term to the right: Add '21.75' to each side of the equation. -21.75 + x + 21.75 + x2 = 0 + 21.75 Reorder the terms: -21.75 + 21.75 + x + x2 = 0 + 21.75 Combine like terms: -21.75 + 21.75 = 0.00 0.00 + x + x2 = 0 + 21.75 x + x2 = 0 + 21.75 Combine like terms: 0 + 21.75 = 21.75 x + x2 = 21.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 21.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 21.75 + 0.25 Combine like terms: 21.75 + 0.25 = 22 1.25 + x2 = 22 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 0.5) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 0.5 = 4.69041576 Simplifying x + 0.5 = 4.69041576 Reorder the terms: 0.5 + x = 4.69041576 Solving 0.5 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.69041576 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.69041576 + -0.5 x = 4.69041576 + -0.5 Combine like terms: 4.69041576 + -0.5 = 4.19041576 x = 4.19041576 Simplifying x = 4.19041576Subproblem 2
x + 0.5 = -4.69041576 Simplifying x + 0.5 = -4.69041576 Reorder the terms: 0.5 + x = -4.69041576 Solving 0.5 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.69041576 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.69041576 + -0.5 x = -4.69041576 + -0.5 Combine like terms: -4.69041576 + -0.5 = -5.19041576 x = -5.19041576 Simplifying x = -5.19041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.19041576, -5.19041576}
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