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Simplifying 6x(3 + 5x) + -2 * 9 = 5x2(7 + -13) + 36 (3 * 6x + 5x * 6x) + -2 * 9 = 5x2(7 + -13) + 36 (18x + 30x2) + -2 * 9 = 5x2(7 + -13) + 36 Multiply -2 * 9 18x + 30x2 + -18 = 5x2(7 + -13) + 36 Reorder the terms: -18 + 18x + 30x2 = 5x2(7 + -13) + 36 Combine like terms: 7 + -13 = -6 -18 + 18x + 30x2 = 5x2(-6) + 36 Reorder the terms for easier multiplication: -18 + 18x + 30x2 = 5 * -6x2 + 36 Multiply 5 * -6 -18 + 18x + 30x2 = -30x2 + 36 Reorder the terms: -18 + 18x + 30x2 = 36 + -30x2 Solving -18 + 18x + 30x2 = 36 + -30x2 Solving for variable 'x'. Reorder the terms: -18 + -36 + 18x + 30x2 + 30x2 = 36 + -30x2 + -36 + 30x2 Combine like terms: -18 + -36 = -54 -54 + 18x + 30x2 + 30x2 = 36 + -30x2 + -36 + 30x2 Combine like terms: 30x2 + 30x2 = 60x2 -54 + 18x + 60x2 = 36 + -30x2 + -36 + 30x2 Reorder the terms: -54 + 18x + 60x2 = 36 + -36 + -30x2 + 30x2 Combine like terms: 36 + -36 = 0 -54 + 18x + 60x2 = 0 + -30x2 + 30x2 -54 + 18x + 60x2 = -30x2 + 30x2 Combine like terms: -30x2 + 30x2 = 0 -54 + 18x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + 3x + 10x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + 3x + 10x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + 10x2 = 0 Solving -9 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.3x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.3x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.3x + x2 = 0.0 + 0.9 0.3x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 0.3x + x2 = 0.9 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.9 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.9 + 0.0225 Combine like terms: 0.9 + 0.0225 = 0.9225 0.0225 + 0.3x + x2 = 0.9225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.9225 Calculate the square root of the right side: 0.960468636 Break this problem into two subproblems by setting (x + 0.15) equal to 0.960468636 and -0.960468636.Subproblem 1
x + 0.15 = 0.960468636 Simplifying x + 0.15 = 0.960468636 Reorder the terms: 0.15 + x = 0.960468636 Solving 0.15 + x = 0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.960468636 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.960468636 + -0.15 x = 0.960468636 + -0.15 Combine like terms: 0.960468636 + -0.15 = 0.810468636 x = 0.810468636 Simplifying x = 0.810468636Subproblem 2
x + 0.15 = -0.960468636 Simplifying x + 0.15 = -0.960468636 Reorder the terms: 0.15 + x = -0.960468636 Solving 0.15 + x = -0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.960468636 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.960468636 + -0.15 x = -0.960468636 + -0.15 Combine like terms: -0.960468636 + -0.15 = -1.110468636 x = -1.110468636 Simplifying x = -1.110468636Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.810468636, -1.110468636}Solution
x = {0.810468636, -1.110468636}
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