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Simplifying 7x + -2x(4x + -3) = 8(9x + -9) + -30 Reorder the terms: 7x + -2x(-3 + 4x) = 8(9x + -9) + -30 7x + (-3 * -2x + 4x * -2x) = 8(9x + -9) + -30 7x + (6x + -8x2) = 8(9x + -9) + -30 Combine like terms: 7x + 6x = 13x 13x + -8x2 = 8(9x + -9) + -30 Reorder the terms: 13x + -8x2 = 8(-9 + 9x) + -30 13x + -8x2 = (-9 * 8 + 9x * 8) + -30 13x + -8x2 = (-72 + 72x) + -30 Reorder the terms: 13x + -8x2 = -72 + -30 + 72x Combine like terms: -72 + -30 = -102 13x + -8x2 = -102 + 72x Solving 13x + -8x2 = -102 + 72x Solving for variable 'x'. Reorder the terms: 102 + 13x + -72x + -8x2 = -102 + 72x + 102 + -72x Combine like terms: 13x + -72x = -59x 102 + -59x + -8x2 = -102 + 72x + 102 + -72x Reorder the terms: 102 + -59x + -8x2 = -102 + 102 + 72x + -72x Combine like terms: -102 + 102 = 0 102 + -59x + -8x2 = 0 + 72x + -72x 102 + -59x + -8x2 = 72x + -72x Combine like terms: 72x + -72x = 0 102 + -59x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.75 + 7.375x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + 7.375x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + 7.375x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + 7.375x + x2 = 0 + 12.75 7.375x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 7.375x + x2 = 12.75 The x term is 7.375x. Take half its coefficient (3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. 7.375x + 13.59765625 + x2 = 12.75 + 13.59765625 Reorder the terms: 13.59765625 + 7.375x + x2 = 12.75 + 13.59765625 Combine like terms: 12.75 + 13.59765625 = 26.34765625 13.59765625 + 7.375x + x2 = 26.34765625 Factor a perfect square on the left side: (x + 3.6875)(x + 3.6875) = 26.34765625 Calculate the square root of the right side: 5.13299681 Break this problem into two subproblems by setting (x + 3.6875) equal to 5.13299681 and -5.13299681.Subproblem 1
x + 3.6875 = 5.13299681 Simplifying x + 3.6875 = 5.13299681 Reorder the terms: 3.6875 + x = 5.13299681 Solving 3.6875 + x = 5.13299681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = 5.13299681 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = 5.13299681 + -3.6875 x = 5.13299681 + -3.6875 Combine like terms: 5.13299681 + -3.6875 = 1.44549681 x = 1.44549681 Simplifying x = 1.44549681Subproblem 2
x + 3.6875 = -5.13299681 Simplifying x + 3.6875 = -5.13299681 Reorder the terms: 3.6875 + x = -5.13299681 Solving 3.6875 + x = -5.13299681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = -5.13299681 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = -5.13299681 + -3.6875 x = -5.13299681 + -3.6875 Combine like terms: -5.13299681 + -3.6875 = -8.82049681 x = -8.82049681 Simplifying x = -8.82049681Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.44549681, -8.82049681}
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