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Simplifying 5x + -4x(x + -8) = 10x + 24 Reorder the terms: 5x + -4x(-8 + x) = 10x + 24 5x + (-8 * -4x + x * -4x) = 10x + 24 5x + (32x + -4x2) = 10x + 24 Combine like terms: 5x + 32x = 37x 37x + -4x2 = 10x + 24 Reorder the terms: 37x + -4x2 = 24 + 10x Solving 37x + -4x2 = 24 + 10x Solving for variable 'x'. Reorder the terms: -24 + 37x + -10x + -4x2 = 24 + 10x + -24 + -10x Combine like terms: 37x + -10x = 27x -24 + 27x + -4x2 = 24 + 10x + -24 + -10x Reorder the terms: -24 + 27x + -4x2 = 24 + -24 + 10x + -10x Combine like terms: 24 + -24 = 0 -24 + 27x + -4x2 = 0 + 10x + -10x -24 + 27x + -4x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -24 + 27x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 6 + -6.75x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6.75x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -6.75x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6.75x + x2 = 0 + -6 -6.75x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6.75x + x2 = -6 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = -6 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -6 + 11.390625 Combine like terms: -6 + 11.390625 = 5.390625 11.390625 + -6.75x + x2 = 5.390625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 5.390625 Calculate the square root of the right side: 2.321771953 Break this problem into two subproblems by setting (x + -3.375) equal to 2.321771953 and -2.321771953.Subproblem 1
x + -3.375 = 2.321771953 Simplifying x + -3.375 = 2.321771953 Reorder the terms: -3.375 + x = 2.321771953 Solving -3.375 + x = 2.321771953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 2.321771953 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 2.321771953 + 3.375 x = 2.321771953 + 3.375 Combine like terms: 2.321771953 + 3.375 = 5.696771953 x = 5.696771953 Simplifying x = 5.696771953Subproblem 2
x + -3.375 = -2.321771953 Simplifying x + -3.375 = -2.321771953 Reorder the terms: -3.375 + x = -2.321771953 Solving -3.375 + x = -2.321771953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -2.321771953 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -2.321771953 + 3.375 x = -2.321771953 + 3.375 Combine like terms: -2.321771953 + 3.375 = 1.053228047 x = 1.053228047 Simplifying x = 1.053228047Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.696771953, 1.053228047}
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