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Simplifying 5(x + 2)(x + -1) = 4 + x Reorder the terms: 5(2 + x)(x + -1) = 4 + x Reorder the terms: 5(2 + x)(-1 + x) = 4 + x Multiply (2 + x) * (-1 + x) 5(2(-1 + x) + x(-1 + x)) = 4 + x 5((-1 * 2 + x * 2) + x(-1 + x)) = 4 + x 5((-2 + 2x) + x(-1 + x)) = 4 + x 5(-2 + 2x + (-1 * x + x * x)) = 4 + x 5(-2 + 2x + (-1x + x2)) = 4 + x Combine like terms: 2x + -1x = 1x 5(-2 + 1x + x2) = 4 + x (-2 * 5 + 1x * 5 + x2 * 5) = 4 + x (-10 + 5x + 5x2) = 4 + x Solving -10 + 5x + 5x2 = 4 + x Solving for variable 'x'. Reorder the terms: -10 + -4 + 5x + -1x + 5x2 = 4 + x + -4 + -1x Combine like terms: -10 + -4 = -14 -14 + 5x + -1x + 5x2 = 4 + x + -4 + -1x Combine like terms: 5x + -1x = 4x -14 + 4x + 5x2 = 4 + x + -4 + -1x Reorder the terms: -14 + 4x + 5x2 = 4 + -4 + x + -1x Combine like terms: 4 + -4 = 0 -14 + 4x + 5x2 = 0 + x + -1x -14 + 4x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -14 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 0.8x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 0.8x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 0.8x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 0.8x + x2 = 0 + 2.8 0.8x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 0.8x + x2 = 2.8 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 2.8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 2.8 + 0.16 Combine like terms: 2.8 + 0.16 = 2.96 0.16 + 0.8x + x2 = 2.96 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (x + 0.4) equal to 1.720465053 and -1.720465053.Subproblem 1
x + 0.4 = 1.720465053 Simplifying x + 0.4 = 1.720465053 Reorder the terms: 0.4 + x = 1.720465053 Solving 0.4 + x = 1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.720465053 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.720465053 + -0.4 x = 1.720465053 + -0.4 Combine like terms: 1.720465053 + -0.4 = 1.320465053 x = 1.320465053 Simplifying x = 1.320465053Subproblem 2
x + 0.4 = -1.720465053 Simplifying x + 0.4 = -1.720465053 Reorder the terms: 0.4 + x = -1.720465053 Solving 0.4 + x = -1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.720465053 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.720465053 + -0.4 x = -1.720465053 + -0.4 Combine like terms: -1.720465053 + -0.4 = -2.120465053 x = -2.120465053 Simplifying x = -2.120465053Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.320465053, -2.120465053}
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