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Simplifying 3x + -5x(x + -5) = -7 + 5x + -24 Reorder the terms: 3x + -5x(-5 + x) = -7 + 5x + -24 3x + (-5 * -5x + x * -5x) = -7 + 5x + -24 3x + (25x + -5x2) = -7 + 5x + -24 Combine like terms: 3x + 25x = 28x 28x + -5x2 = -7 + 5x + -24 Reorder the terms: 28x + -5x2 = -7 + -24 + 5x Combine like terms: -7 + -24 = -31 28x + -5x2 = -31 + 5x Solving 28x + -5x2 = -31 + 5x Solving for variable 'x'. Reorder the terms: 31 + 28x + -5x + -5x2 = -31 + 5x + 31 + -5x Combine like terms: 28x + -5x = 23x 31 + 23x + -5x2 = -31 + 5x + 31 + -5x Reorder the terms: 31 + 23x + -5x2 = -31 + 31 + 5x + -5x Combine like terms: -31 + 31 = 0 31 + 23x + -5x2 = 0 + 5x + -5x 31 + 23x + -5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 31 + 23x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6.2 + -4.6x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + -4.6x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + -4.6x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + -4.6x + x2 = 0 + 6.2 -4.6x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 -4.6x + x2 = 6.2 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 6.2 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 6.2 + 5.29 Combine like terms: 6.2 + 5.29 = 11.49 5.29 + -4.6x + x2 = 11.49 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 11.49 Calculate the square root of the right side: 3.389690251 Break this problem into two subproblems by setting (x + -2.3) equal to 3.389690251 and -3.389690251.Subproblem 1
x + -2.3 = 3.389690251 Simplifying x + -2.3 = 3.389690251 Reorder the terms: -2.3 + x = 3.389690251 Solving -2.3 + x = 3.389690251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 3.389690251 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 3.389690251 + 2.3 x = 3.389690251 + 2.3 Combine like terms: 3.389690251 + 2.3 = 5.689690251 x = 5.689690251 Simplifying x = 5.689690251Subproblem 2
x + -2.3 = -3.389690251 Simplifying x + -2.3 = -3.389690251 Reorder the terms: -2.3 + x = -3.389690251 Solving -2.3 + x = -3.389690251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -3.389690251 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -3.389690251 + 2.3 x = -3.389690251 + 2.3 Combine like terms: -3.389690251 + 2.3 = -1.089690251 x = -1.089690251 Simplifying x = -1.089690251Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.689690251, -1.089690251}
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