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Simplifying (7x + 4) * 2x + 7x + 4 + (7x + 4) + -4 = 180 Reorder the terms: (4 + 7x) * 2x + 7x + 4 + (7x + 4) + -4 = 180 Reorder the terms for easier multiplication: 2x(4 + 7x) + 7x + 4 + (7x + 4) + -4 = 180 (4 * 2x + 7x * 2x) + 7x + 4 + (7x + 4) + -4 = 180 (8x + 14x2) + 7x + 4 + (7x + 4) + -4 = 180 Reorder the terms: 8x + 14x2 + 7x + 4 + (4 + 7x) + -4 = 180 Remove parenthesis around (4 + 7x) 8x + 14x2 + 7x + 4 + 4 + 7x + -4 = 180 Reorder the terms: 4 + 4 + -4 + 8x + 7x + 7x + 14x2 = 180 Combine like terms: 4 + 4 = 8 8 + -4 + 8x + 7x + 7x + 14x2 = 180 Combine like terms: 8 + -4 = 4 4 + 8x + 7x + 7x + 14x2 = 180 Combine like terms: 8x + 7x = 15x 4 + 15x + 7x + 14x2 = 180 Combine like terms: 15x + 7x = 22x 4 + 22x + 14x2 = 180 Solving 4 + 22x + 14x2 = 180 Solving for variable 'x'. Reorder the terms: 4 + -180 + 22x + 14x2 = 180 + -180 Combine like terms: 4 + -180 = -176 -176 + 22x + 14x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -176 + 22x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-88 + 11x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-88 + 11x + 7x2)' equal to zero and attempt to solve: Simplifying -88 + 11x + 7x2 = 0 Solving -88 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -12.57142857 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '12.57142857' to each side of the equation. -12.57142857 + 1.571428571x + 12.57142857 + x2 = 0 + 12.57142857 Reorder the terms: -12.57142857 + 12.57142857 + 1.571428571x + x2 = 0 + 12.57142857 Combine like terms: -12.57142857 + 12.57142857 = 0.00000000 0.00000000 + 1.571428571x + x2 = 0 + 12.57142857 1.571428571x + x2 = 0 + 12.57142857 Combine like terms: 0 + 12.57142857 = 12.57142857 1.571428571x + x2 = 12.57142857 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 12.57142857 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 12.57142857 + 0.6173469384 Combine like terms: 12.57142857 + 0.6173469384 = 13.1887755084 0.6173469384 + 1.571428571x + x2 = 13.1887755084 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 13.1887755084 Calculate the square root of the right side: 3.631635377 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 3.631635377 and -3.631635377.Subproblem 1
x + 0.7857142855 = 3.631635377 Simplifying x + 0.7857142855 = 3.631635377 Reorder the terms: 0.7857142855 + x = 3.631635377 Solving 0.7857142855 + x = 3.631635377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 3.631635377 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 3.631635377 + -0.7857142855 x = 3.631635377 + -0.7857142855 Combine like terms: 3.631635377 + -0.7857142855 = 2.8459210915 x = 2.8459210915 Simplifying x = 2.8459210915Subproblem 2
x + 0.7857142855 = -3.631635377 Simplifying x + 0.7857142855 = -3.631635377 Reorder the terms: 0.7857142855 + x = -3.631635377 Solving 0.7857142855 + x = -3.631635377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -3.631635377 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -3.631635377 + -0.7857142855 x = -3.631635377 + -0.7857142855 Combine like terms: -3.631635377 + -0.7857142855 = -4.4173496625 x = -4.4173496625 Simplifying x = -4.4173496625Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8459210915, -4.4173496625}Solution
x = {2.8459210915, -4.4173496625}
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