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Simplifying 4(x2 + -8x) + -63 = 0 Reorder the terms: 4(-8x + x2) + -63 = 0 (-8x * 4 + x2 * 4) + -63 = 0 (-32x + 4x2) + -63 = 0 Reorder the terms: -63 + -32x + 4x2 = 0 Solving -63 + -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'. -15.75 + -8x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -8x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -8x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -8x + x2 = 0 + 15.75 -8x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -8x + x2 = 15.75 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 = 15.75 + 16 Reorder the terms: 16 + -8x + x2 = 15.75 + 16 Combine like terms: 15.75 + 16 = 31.75 16 + -8x + x2 = 31.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (x + -4) equal to 5.634713835 and -5.634713835.Subproblem 1
x + -4 = 5.634713835 Simplifying x + -4 = 5.634713835 Reorder the terms: -4 + x = 5.634713835 Solving -4 + x = 5.634713835 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 = 5.634713835 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.634713835 + 4 x = 5.634713835 + 4 Combine like terms: 5.634713835 + 4 = 9.634713835 x = 9.634713835 Simplifying x = 9.634713835Subproblem 2
x + -4 = -5.634713835 Simplifying x + -4 = -5.634713835 Reorder the terms: -4 + x = -5.634713835 Solving -4 + x = -5.634713835 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 = -5.634713835 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.634713835 + 4 x = -5.634713835 + 4 Combine like terms: -5.634713835 + 4 = -1.634713835 x = -1.634713835 Simplifying x = -1.634713835Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.634713835, -1.634713835}
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