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Simplifying 5(2x + -1) + -1(10x2 + -6) = -1(x + 2) Reorder the terms: 5(-1 + 2x) + -1(10x2 + -6) = -1(x + 2) (-1 * 5 + 2x * 5) + -1(10x2 + -6) = -1(x + 2) (-5 + 10x) + -1(10x2 + -6) = -1(x + 2) Reorder the terms: -5 + 10x + -1(-6 + 10x2) = -1(x + 2) -5 + 10x + (-6 * -1 + 10x2 * -1) = -1(x + 2) -5 + 10x + (6 + -10x2) = -1(x + 2) Reorder the terms: -5 + 6 + 10x + -10x2 = -1(x + 2) Combine like terms: -5 + 6 = 1 1 + 10x + -10x2 = -1(x + 2) Reorder the terms: 1 + 10x + -10x2 = -1(2 + x) 1 + 10x + -10x2 = (2 * -1 + x * -1) 1 + 10x + -10x2 = (-2 + -1x) Solving 1 + 10x + -10x2 = -2 + -1x Solving for variable 'x'. Reorder the terms: 1 + 2 + 10x + x + -10x2 = -2 + -1x + 2 + x Combine like terms: 1 + 2 = 3 3 + 10x + x + -10x2 = -2 + -1x + 2 + x Combine like terms: 10x + x = 11x 3 + 11x + -10x2 = -2 + -1x + 2 + x Reorder the terms: 3 + 11x + -10x2 = -2 + 2 + -1x + x Combine like terms: -2 + 2 = 0 3 + 11x + -10x2 = 0 + -1x + x 3 + 11x + -10x2 = -1x + x Combine like terms: -1x + x = 0 3 + 11x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + -1.1x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.1x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.1x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.1x + x2 = 0.0 + 0.3 -1.1x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -1.1x + x2 = 0.3 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 0.3 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 0.3 + 0.3025 Combine like terms: 0.3 + 0.3025 = 0.6025 0.3025 + -1.1x + x2 = 0.6025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + -0.55) equal to 0.776208735 and -0.776208735.Subproblem 1
x + -0.55 = 0.776208735 Simplifying x + -0.55 = 0.776208735 Reorder the terms: -0.55 + x = 0.776208735 Solving -0.55 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.776208735 + 0.55 x = 0.776208735 + 0.55 Combine like terms: 0.776208735 + 0.55 = 1.326208735 x = 1.326208735 Simplifying x = 1.326208735Subproblem 2
x + -0.55 = -0.776208735 Simplifying x + -0.55 = -0.776208735 Reorder the terms: -0.55 + x = -0.776208735 Solving -0.55 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.776208735 + 0.55 x = -0.776208735 + 0.55 Combine like terms: -0.776208735 + 0.55 = -0.226208735 x = -0.226208735 Simplifying x = -0.226208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.326208735, -0.226208735}
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