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Simplifying 5x(-2x + -2) = x + (3x + -5) Reorder the terms: 5x(-2 + -2x) = x + (3x + -5) (-2 * 5x + -2x * 5x) = x + (3x + -5) (-10x + -10x2) = x + (3x + -5) Reorder the terms: -10x + -10x2 = x + (-5 + 3x) Remove parenthesis around (-5 + 3x) -10x + -10x2 = x + -5 + 3x Reorder the terms: -10x + -10x2 = -5 + x + 3x Combine like terms: x + 3x = 4x -10x + -10x2 = -5 + 4x Solving -10x + -10x2 = -5 + 4x Solving for variable 'x'. Reorder the terms: 5 + -10x + -4x + -10x2 = -5 + 4x + 5 + -4x Combine like terms: -10x + -4x = -14x 5 + -14x + -10x2 = -5 + 4x + 5 + -4x Reorder the terms: 5 + -14x + -10x2 = -5 + 5 + 4x + -4x Combine like terms: -5 + 5 = 0 5 + -14x + -10x2 = 0 + 4x + -4x 5 + -14x + -10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 5 + -14x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.5 + 1.4x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.4x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.4x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.4x + x2 = 0.0 + 0.5 1.4x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 1.4x + x2 = 0.5 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 0.5 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 0.5 + 0.49 Combine like terms: 0.5 + 0.49 = 0.99 0.49 + 1.4x + x2 = 0.99 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + 0.7) equal to 0.994987437 and -0.994987437.Subproblem 1
x + 0.7 = 0.994987437 Simplifying x + 0.7 = 0.994987437 Reorder the terms: 0.7 + x = 0.994987437 Solving 0.7 + x = 0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.994987437 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.994987437 + -0.7 x = 0.994987437 + -0.7 Combine like terms: 0.994987437 + -0.7 = 0.294987437 x = 0.294987437 Simplifying x = 0.294987437Subproblem 2
x + 0.7 = -0.994987437 Simplifying x + 0.7 = -0.994987437 Reorder the terms: 0.7 + x = -0.994987437 Solving 0.7 + x = -0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.994987437 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.994987437 + -0.7 x = -0.994987437 + -0.7 Combine like terms: -0.994987437 + -0.7 = -1.694987437 x = -1.694987437 Simplifying x = -1.694987437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.294987437, -1.694987437}
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