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Simplifying x = (x + 3)(5x + -1) + -2x Reorder the terms: x = (3 + x)(5x + -1) + -2x Reorder the terms: x = (3 + x)(-1 + 5x) + -2x Multiply (3 + x) * (-1 + 5x) x = (3(-1 + 5x) + x(-1 + 5x)) + -2x x = ((-1 * 3 + 5x * 3) + x(-1 + 5x)) + -2x x = ((-3 + 15x) + x(-1 + 5x)) + -2x x = (-3 + 15x + (-1 * x + 5x * x)) + -2x x = (-3 + 15x + (-1x + 5x2)) + -2x Combine like terms: 15x + -1x = 14x x = (-3 + 14x + 5x2) + -2x Reorder the terms: x = -3 + 14x + -2x + 5x2 Combine like terms: 14x + -2x = 12x x = -3 + 12x + 5x2 Solving x = -3 + 12x + 5x2 Solving for variable 'x'. Reorder the terms: 3 + x + -12x + -5x2 = -3 + 12x + 5x2 + 3 + -12x + -5x2 Combine like terms: x + -12x = -11x 3 + -11x + -5x2 = -3 + 12x + 5x2 + 3 + -12x + -5x2 Reorder the terms: 3 + -11x + -5x2 = -3 + 3 + 12x + -12x + 5x2 + -5x2 Combine like terms: -3 + 3 = 0 3 + -11x + -5x2 = 0 + 12x + -12x + 5x2 + -5x2 3 + -11x + -5x2 = 12x + -12x + 5x2 + -5x2 Combine like terms: 12x + -12x = 0 3 + -11x + -5x2 = 0 + 5x2 + -5x2 3 + -11x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 3 + -11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + 2.2x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2.2x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2.2x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2.2x + x2 = 0 + 0.6 2.2x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2.2x + x2 = 0.6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 0.6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 0.6 + 1.21 Combine like terms: 0.6 + 1.21 = 1.81 1.21 + 2.2x + x2 = 1.81 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 1.81 Calculate the square root of the right side: 1.345362405 Break this problem into two subproblems by setting (x + 1.1) equal to 1.345362405 and -1.345362405.Subproblem 1
x + 1.1 = 1.345362405 Simplifying x + 1.1 = 1.345362405 Reorder the terms: 1.1 + x = 1.345362405 Solving 1.1 + x = 1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.345362405 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.345362405 + -1.1 x = 1.345362405 + -1.1 Combine like terms: 1.345362405 + -1.1 = 0.245362405 x = 0.245362405 Simplifying x = 0.245362405Subproblem 2
x + 1.1 = -1.345362405 Simplifying x + 1.1 = -1.345362405 Reorder the terms: 1.1 + x = -1.345362405 Solving 1.1 + x = -1.345362405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.345362405 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.345362405 + -1.1 x = -1.345362405 + -1.1 Combine like terms: -1.345362405 + -1.1 = -2.445362405 x = -2.445362405 Simplifying x = -2.445362405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.245362405, -2.445362405}
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