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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 (-4 * 5 + x * 5) + 3x + -9x = 6 + -1(2x + 5) * 8x (-20 + 5x) + 3x + -9x = 6 + -1(2x + 5) * 8x Combine like terms: 5x + 3x = 8x -20 + 8x + -9x = 6 + -1(2x + 5) * 8x Combine like terms: 8x + -9x = -1x -20 + -1x = 6 + -1(2x + 5) * 8x Reorder the terms: -20 + -1x = 6 + -1(5 + 2x) * 8x Reorder the terms for easier multiplication: -20 + -1x = 6 + -1 * 8x(5 + 2x) Multiply -1 * 8 -20 + -1x = 6 + -8x(5 + 2x) -20 + -1x = 6 + (5 * -8x + 2x * -8x) -20 + -1x = 6 + (-40x + -16x2) Solving -20 + -1x = 6 + -40x + -16x2 Solving for variable 'x'. Reorder the terms: -20 + -6 + -1x + 40x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2 Combine like terms: -20 + -6 = -26 -26 + -1x + 40x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2 Combine like terms: -1x + 40x = 39x -26 + 39x + 16x2 = 6 + -40x + -16x2 + -6 + 40x + 16x2 Reorder the terms: -26 + 39x + 16x2 = 6 + -6 + -40x + 40x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -26 + 39x + 16x2 = 0 + -40x + 40x + -16x2 + 16x2 -26 + 39x + 16x2 = -40x + 40x + -16x2 + 16x2 Combine like terms: -40x + 40x = 0 -26 + 39x + 16x2 = 0 + -16x2 + 16x2 -26 + 39x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -26 + 39x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.625 + 2.4375x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 2.4375x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 2.4375x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 2.4375x + x2 = 0 + 1.625 2.4375x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 2.4375x + x2 = 1.625 The x term is 2.4375x. Take half its coefficient (1.21875). Square it (1.485351563) and add it to both sides. Add '1.485351563' to each side of the equation. 2.4375x + 1.485351563 + x2 = 1.625 + 1.485351563 Reorder the terms: 1.485351563 + 2.4375x + x2 = 1.625 + 1.485351563 Combine like terms: 1.625 + 1.485351563 = 3.110351563 1.485351563 + 2.4375x + x2 = 3.110351563 Factor a perfect square on the left side: (x + 1.21875)(x + 1.21875) = 3.110351563 Calculate the square root of the right side: 1.763618883 Break this problem into two subproblems by setting (x + 1.21875) equal to 1.763618883 and -1.763618883.Subproblem 1
x + 1.21875 = 1.763618883 Simplifying x + 1.21875 = 1.763618883 Reorder the terms: 1.21875 + x = 1.763618883 Solving 1.21875 + x = 1.763618883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.21875' to each side of the equation. 1.21875 + -1.21875 + x = 1.763618883 + -1.21875 Combine like terms: 1.21875 + -1.21875 = 0.00000 0.00000 + x = 1.763618883 + -1.21875 x = 1.763618883 + -1.21875 Combine like terms: 1.763618883 + -1.21875 = 0.544868883 x = 0.544868883 Simplifying x = 0.544868883Subproblem 2
x + 1.21875 = -1.763618883 Simplifying x + 1.21875 = -1.763618883 Reorder the terms: 1.21875 + x = -1.763618883 Solving 1.21875 + x = -1.763618883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.21875' to each side of the equation. 1.21875 + -1.21875 + x = -1.763618883 + -1.21875 Combine like terms: 1.21875 + -1.21875 = 0.00000 0.00000 + x = -1.763618883 + -1.21875 x = -1.763618883 + -1.21875 Combine like terms: -1.763618883 + -1.21875 = -2.982368883 x = -2.982368883 Simplifying x = -2.982368883Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.544868883, -2.982368883}
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