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Simplifying 8x2 + 56x + -63 = 0 Reorder the terms: -63 + 56x + 8x2 = 0 Solving -63 + 56x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.875 + 7x + x2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + 7x + 7.875 + x2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + 7x + x2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + 7x + x2 = 0 + 7.875 7x + x2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 7x + x2 = 7.875 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 7.875 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 7.875 + 12.25 Combine like terms: 7.875 + 12.25 = 20.125 12.25 + 7x + x2 = 20.125 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 20.125 Calculate the square root of the right side: 4.486089611 Break this problem into two subproblems by setting (x + 3.5) equal to 4.486089611 and -4.486089611.Subproblem 1
x + 3.5 = 4.486089611 Simplifying x + 3.5 = 4.486089611 Reorder the terms: 3.5 + x = 4.486089611 Solving 3.5 + x = 4.486089611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.486089611 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.486089611 + -3.5 x = 4.486089611 + -3.5 Combine like terms: 4.486089611 + -3.5 = 0.986089611 x = 0.986089611 Simplifying x = 0.986089611Subproblem 2
x + 3.5 = -4.486089611 Simplifying x + 3.5 = -4.486089611 Reorder the terms: 3.5 + x = -4.486089611 Solving 3.5 + x = -4.486089611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.486089611 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.486089611 + -3.5 x = -4.486089611 + -3.5 Combine like terms: -4.486089611 + -3.5 = -7.986089611 x = -7.986089611 Simplifying x = -7.986089611Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.986089611, -7.986089611}
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