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Simplifying 4x2 + -32x + 59 = 0 Reorder the terms: 59 + -32x + 4x2 = 0 Solving 59 + -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'. 14.75 + -8x + x2 = 0 Move the constant term to the right: Add '-14.75' to each side of the equation. 14.75 + -8x + -14.75 + x2 = 0 + -14.75 Reorder the terms: 14.75 + -14.75 + -8x + x2 = 0 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + -8x + x2 = 0 + -14.75 -8x + x2 = 0 + -14.75 Combine like terms: 0 + -14.75 = -14.75 -8x + x2 = -14.75 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 = -14.75 + 16 Reorder the terms: 16 + -8x + x2 = -14.75 + 16 Combine like terms: -14.75 + 16 = 1.25 16 + -8x + x2 = 1.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -4) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -4 = 1.118033989 Simplifying x + -4 = 1.118033989 Reorder the terms: -4 + x = 1.118033989 Solving -4 + x = 1.118033989 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 = 1.118033989 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.118033989 + 4 x = 1.118033989 + 4 Combine like terms: 1.118033989 + 4 = 5.118033989 x = 5.118033989 Simplifying x = 5.118033989Subproblem 2
x + -4 = -1.118033989 Simplifying x + -4 = -1.118033989 Reorder the terms: -4 + x = -1.118033989 Solving -4 + x = -1.118033989 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 = -1.118033989 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.118033989 + 4 x = -1.118033989 + 4 Combine like terms: -1.118033989 + 4 = 2.881966011 x = 2.881966011 Simplifying x = 2.881966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.118033989, 2.881966011}
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