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Simplifying 8x2 + 7x + -75 = 0 Reorder the terms: -75 + 7x + 8x2 = 0 Solving -75 + 7x + 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'. -9.375 + 0.875x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 0.875x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 0.875x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 0.875x + x2 = 0 + 9.375 0.875x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 0.875x + x2 = 9.375 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 9.375 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 9.375 + 0.19140625 Combine like terms: 9.375 + 0.19140625 = 9.56640625 0.19140625 + 0.875x + x2 = 9.56640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 9.56640625 Calculate the square root of the right side: 3.092960758 Break this problem into two subproblems by setting (x + 0.4375) equal to 3.092960758 and -3.092960758.Subproblem 1
x + 0.4375 = 3.092960758 Simplifying x + 0.4375 = 3.092960758 Reorder the terms: 0.4375 + x = 3.092960758 Solving 0.4375 + x = 3.092960758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 3.092960758 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 3.092960758 + -0.4375 x = 3.092960758 + -0.4375 Combine like terms: 3.092960758 + -0.4375 = 2.655460758 x = 2.655460758 Simplifying x = 2.655460758Subproblem 2
x + 0.4375 = -3.092960758 Simplifying x + 0.4375 = -3.092960758 Reorder the terms: 0.4375 + x = -3.092960758 Solving 0.4375 + x = -3.092960758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -3.092960758 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -3.092960758 + -0.4375 x = -3.092960758 + -0.4375 Combine like terms: -3.092960758 + -0.4375 = -3.530460758 x = -3.530460758 Simplifying x = -3.530460758Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.655460758, -3.530460758}
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