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Simplifying x(8x + -7) = 16 Reorder the terms: x(-7 + 8x) = 16 (-7 * x + 8x * x) = 16 (-7x + 8x2) = 16 Solving -7x + 8x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -7x + 8x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + -0.875x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.875x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.875x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.875x + x2 = 0 + 2 -0.875x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.875x + x2 = 2 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 = 2 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 2 + 0.19140625 Combine like terms: 2 + 0.19140625 = 2.19140625 0.19140625 + -0.875x + x2 = 2.19140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 2.19140625 Calculate the square root of the right side: 1.48033991 Break this problem into two subproblems by setting (x + -0.4375) equal to 1.48033991 and -1.48033991.Subproblem 1
x + -0.4375 = 1.48033991 Simplifying x + -0.4375 = 1.48033991 Reorder the terms: -0.4375 + x = 1.48033991 Solving -0.4375 + x = 1.48033991 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 = 1.48033991 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 1.48033991 + 0.4375 x = 1.48033991 + 0.4375 Combine like terms: 1.48033991 + 0.4375 = 1.91783991 x = 1.91783991 Simplifying x = 1.91783991Subproblem 2
x + -0.4375 = -1.48033991 Simplifying x + -0.4375 = -1.48033991 Reorder the terms: -0.4375 + x = -1.48033991 Solving -0.4375 + x = -1.48033991 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 = -1.48033991 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -1.48033991 + 0.4375 x = -1.48033991 + 0.4375 Combine like terms: -1.48033991 + 0.4375 = -1.04283991 x = -1.04283991 Simplifying x = -1.04283991Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.91783991, -1.04283991}
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