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Simplifying 2x(x + -1) + -5(x + 2) = -3(x + -9) Reorder the terms: 2x(-1 + x) + -5(x + 2) = -3(x + -9) (-1 * 2x + x * 2x) + -5(x + 2) = -3(x + -9) (-2x + 2x2) + -5(x + 2) = -3(x + -9) Reorder the terms: -2x + 2x2 + -5(2 + x) = -3(x + -9) -2x + 2x2 + (2 * -5 + x * -5) = -3(x + -9) -2x + 2x2 + (-10 + -5x) = -3(x + -9) Reorder the terms: -10 + -2x + -5x + 2x2 = -3(x + -9) Combine like terms: -2x + -5x = -7x -10 + -7x + 2x2 = -3(x + -9) Reorder the terms: -10 + -7x + 2x2 = -3(-9 + x) -10 + -7x + 2x2 = (-9 * -3 + x * -3) -10 + -7x + 2x2 = (27 + -3x) Solving -10 + -7x + 2x2 = 27 + -3x Solving for variable 'x'. Reorder the terms: -10 + -27 + -7x + 3x + 2x2 = 27 + -3x + -27 + 3x Combine like terms: -10 + -27 = -37 -37 + -7x + 3x + 2x2 = 27 + -3x + -27 + 3x Combine like terms: -7x + 3x = -4x -37 + -4x + 2x2 = 27 + -3x + -27 + 3x Reorder the terms: -37 + -4x + 2x2 = 27 + -27 + -3x + 3x Combine like terms: 27 + -27 = 0 -37 + -4x + 2x2 = 0 + -3x + 3x -37 + -4x + 2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -37 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18.5 + -2x + x2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -2x + 18.5 + x2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -2x + x2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -2x + x2 = 0 + 18.5 -2x + x2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -2x + x2 = 18.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 18.5 + 1 Reorder the terms: 1 + -2x + x2 = 18.5 + 1 Combine like terms: 18.5 + 1 = 19.5 1 + -2x + x2 = 19.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + -1) equal to 4.415880433 and -4.415880433.Subproblem 1
x + -1 = 4.415880433 Simplifying x + -1 = 4.415880433 Reorder the terms: -1 + x = 4.415880433 Solving -1 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.415880433 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.415880433 + 1 x = 4.415880433 + 1 Combine like terms: 4.415880433 + 1 = 5.415880433 x = 5.415880433 Simplifying x = 5.415880433Subproblem 2
x + -1 = -4.415880433 Simplifying x + -1 = -4.415880433 Reorder the terms: -1 + x = -4.415880433 Solving -1 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.415880433 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.415880433 + 1 x = -4.415880433 + 1 Combine like terms: -4.415880433 + 1 = -3.415880433 x = -3.415880433 Simplifying x = -3.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.415880433, -3.415880433}
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