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Simplifying 8x(-10 + -4x) = 7x + -16 (-10 * 8x + -4x * 8x) = 7x + -16 (-80x + -32x2) = 7x + -16 Reorder the terms: -80x + -32x2 = -16 + 7x Solving -80x + -32x2 = -16 + 7x Solving for variable 'x'. Reorder the terms: 16 + -80x + -7x + -32x2 = -16 + 7x + 16 + -7x Combine like terms: -80x + -7x = -87x 16 + -87x + -32x2 = -16 + 7x + 16 + -7x Reorder the terms: 16 + -87x + -32x2 = -16 + 16 + 7x + -7x Combine like terms: -16 + 16 = 0 16 + -87x + -32x2 = 0 + 7x + -7x 16 + -87x + -32x2 = 7x + -7x Combine like terms: 7x + -7x = 0 16 + -87x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -0.5 + 2.71875x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.71875x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.71875x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.71875x + x2 = 0 + 0.5 2.71875x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.71875x + x2 = 0.5 The x term is 2.71875x. Take half its coefficient (1.359375). Square it (1.847900391) and add it to both sides. Add '1.847900391' to each side of the equation. 2.71875x + 1.847900391 + x2 = 0.5 + 1.847900391 Reorder the terms: 1.847900391 + 2.71875x + x2 = 0.5 + 1.847900391 Combine like terms: 0.5 + 1.847900391 = 2.347900391 1.847900391 + 2.71875x + x2 = 2.347900391 Factor a perfect square on the left side: (x + 1.359375)(x + 1.359375) = 2.347900391 Calculate the square root of the right side: 1.532286002 Break this problem into two subproblems by setting (x + 1.359375) equal to 1.532286002 and -1.532286002.Subproblem 1
x + 1.359375 = 1.532286002 Simplifying x + 1.359375 = 1.532286002 Reorder the terms: 1.359375 + x = 1.532286002 Solving 1.359375 + x = 1.532286002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.359375' to each side of the equation. 1.359375 + -1.359375 + x = 1.532286002 + -1.359375 Combine like terms: 1.359375 + -1.359375 = 0.000000 0.000000 + x = 1.532286002 + -1.359375 x = 1.532286002 + -1.359375 Combine like terms: 1.532286002 + -1.359375 = 0.172911002 x = 0.172911002 Simplifying x = 0.172911002Subproblem 2
x + 1.359375 = -1.532286002 Simplifying x + 1.359375 = -1.532286002 Reorder the terms: 1.359375 + x = -1.532286002 Solving 1.359375 + x = -1.532286002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.359375' to each side of the equation. 1.359375 + -1.359375 + x = -1.532286002 + -1.359375 Combine like terms: 1.359375 + -1.359375 = 0.000000 0.000000 + x = -1.532286002 + -1.359375 x = -1.532286002 + -1.359375 Combine like terms: -1.532286002 + -1.359375 = -2.891661002 x = -2.891661002 Simplifying x = -2.891661002Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.172911002, -2.891661002}
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