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Simplifying (10x)(6x + 8) = 4200 Remove parenthesis around (10x) 10x(6x + 8) = 4200 Reorder the terms: 10x(8 + 6x) = 4200 (8 * 10x + 6x * 10x) = 4200 (80x + 60x2) = 4200 Solving 80x + 60x2 = 4200 Solving for variable 'x'. Reorder the terms: -4200 + 80x + 60x2 = 4200 + -4200 Combine like terms: 4200 + -4200 = 0 -4200 + 80x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-210 + 4x + 3x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-210 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -210 + 4x + 3x2 = 0 Solving -210 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -70 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 1.333333333x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 1.333333333x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 1.333333333x + x2 = 0 + 70 1.333333333x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 1.333333333x + x2 = 70 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 70 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 70 + 0.4444444442 Combine like terms: 70 + 0.4444444442 = 70.4444444442 0.4444444442 + 1.333333333x + x2 = 70.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 70.4444444442 Calculate the square root of the right side: 8.393118875 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 8.393118875 and -8.393118875.Subproblem 1
x + 0.6666666665 = 8.393118875 Simplifying x + 0.6666666665 = 8.393118875 Reorder the terms: 0.6666666665 + x = 8.393118875 Solving 0.6666666665 + x = 8.393118875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 8.393118875 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 8.393118875 + -0.6666666665 x = 8.393118875 + -0.6666666665 Combine like terms: 8.393118875 + -0.6666666665 = 7.7264522085 x = 7.7264522085 Simplifying x = 7.7264522085Subproblem 2
x + 0.6666666665 = -8.393118875 Simplifying x + 0.6666666665 = -8.393118875 Reorder the terms: 0.6666666665 + x = -8.393118875 Solving 0.6666666665 + x = -8.393118875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -8.393118875 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -8.393118875 + -0.6666666665 x = -8.393118875 + -0.6666666665 Combine like terms: -8.393118875 + -0.6666666665 = -9.0597855415 x = -9.0597855415 Simplifying x = -9.0597855415Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.7264522085, -9.0597855415}Solution
x = {7.7264522085, -9.0597855415}
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