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Simplifying 5(x + -1) + -2(2x2 + -7x) = -8 Reorder the terms: 5(-1 + x) + -2(2x2 + -7x) = -8 (-1 * 5 + x * 5) + -2(2x2 + -7x) = -8 (-5 + 5x) + -2(2x2 + -7x) = -8 Reorder the terms: -5 + 5x + -2(-7x + 2x2) = -8 -5 + 5x + (-7x * -2 + 2x2 * -2) = -8 -5 + 5x + (14x + -4x2) = -8 Combine like terms: 5x + 14x = 19x -5 + 19x + -4x2 = -8 Solving -5 + 19x + -4x2 = -8 Solving for variable 'x'. Reorder the terms: -5 + 8 + 19x + -4x2 = -8 + 8 Combine like terms: -5 + 8 = 3 3 + 19x + -4x2 = -8 + 8 Combine like terms: -8 + 8 = 0 3 + 19x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -4.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -4.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -4.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -4.75x + x2 = 0 + 0.75 -4.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -4.75x + x2 = 0.75 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 0.75 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 0.75 + 5.640625 Combine like terms: 0.75 + 5.640625 = 6.390625 5.640625 + -4.75x + x2 = 6.390625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + -2.375) equal to 2.527968552 and -2.527968552.Subproblem 1
x + -2.375 = 2.527968552 Simplifying x + -2.375 = 2.527968552 Reorder the terms: -2.375 + x = 2.527968552 Solving -2.375 + x = 2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.527968552 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.527968552 + 2.375 x = 2.527968552 + 2.375 Combine like terms: 2.527968552 + 2.375 = 4.902968552 x = 4.902968552 Simplifying x = 4.902968552Subproblem 2
x + -2.375 = -2.527968552 Simplifying x + -2.375 = -2.527968552 Reorder the terms: -2.375 + x = -2.527968552 Solving -2.375 + x = -2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.527968552 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.527968552 + 2.375 x = -2.527968552 + 2.375 Combine like terms: -2.527968552 + 2.375 = -0.152968552 x = -0.152968552 Simplifying x = -0.152968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.902968552, -0.152968552}
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