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Simplifying 5(x + -4) * 3x + -9x = 6 + -1(2x + 5) + 8x Reorder the terms: 5(-4 + x) * 3x + -9x = 6 + -1(2x + 5) + 8x Reorder the terms for easier multiplication: 5 * 3x(-4 + x) + -9x = 6 + -1(2x + 5) + 8x Multiply 5 * 3 15x(-4 + x) + -9x = 6 + -1(2x + 5) + 8x (-4 * 15x + x * 15x) + -9x = 6 + -1(2x + 5) + 8x (-60x + 15x2) + -9x = 6 + -1(2x + 5) + 8x Reorder the terms: -60x + -9x + 15x2 = 6 + -1(2x + 5) + 8x Combine like terms: -60x + -9x = -69x -69x + 15x2 = 6 + -1(2x + 5) + 8x Reorder the terms: -69x + 15x2 = 6 + -1(5 + 2x) + 8x -69x + 15x2 = 6 + (5 * -1 + 2x * -1) + 8x -69x + 15x2 = 6 + (-5 + -2x) + 8x Combine like terms: 6 + -5 = 1 -69x + 15x2 = 1 + -2x + 8x Combine like terms: -2x + 8x = 6x -69x + 15x2 = 1 + 6x Solving -69x + 15x2 = 1 + 6x Solving for variable 'x'. Reorder the terms: -1 + -69x + -6x + 15x2 = 1 + 6x + -1 + -6x Combine like terms: -69x + -6x = -75x -1 + -75x + 15x2 = 1 + 6x + -1 + -6x Reorder the terms: -1 + -75x + 15x2 = 1 + -1 + 6x + -6x Combine like terms: 1 + -1 = 0 -1 + -75x + 15x2 = 0 + 6x + -6x -1 + -75x + 15x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1 + -75x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.06666666667 + -5x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -5x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -5x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -5x + x2 = 0 + 0.06666666667 -5x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -5x + x2 = 0.06666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.06666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.06666666667 + 6.25 Combine like terms: 0.06666666667 + 6.25 = 6.31666666667 6.25 + -5x + x2 = 6.31666666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.31666666667 Calculate the square root of the right side: 2.513297966 Break this problem into two subproblems by setting (x + -2.5) equal to 2.513297966 and -2.513297966.Subproblem 1
x + -2.5 = 2.513297966 Simplifying x + -2.5 = 2.513297966 Reorder the terms: -2.5 + x = 2.513297966 Solving -2.5 + x = 2.513297966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.513297966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.513297966 + 2.5 x = 2.513297966 + 2.5 Combine like terms: 2.513297966 + 2.5 = 5.013297966 x = 5.013297966 Simplifying x = 5.013297966Subproblem 2
x + -2.5 = -2.513297966 Simplifying x + -2.5 = -2.513297966 Reorder the terms: -2.5 + x = -2.513297966 Solving -2.5 + x = -2.513297966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.513297966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.513297966 + 2.5 x = -2.513297966 + 2.5 Combine like terms: -2.513297966 + 2.5 = -0.013297966 x = -0.013297966 Simplifying x = -0.013297966Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.013297966, -0.013297966}
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