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Simplifying 120 + -1(12x2) + -1(88x) = 0 Remove parenthesis around (12x2) 120 + -1 * 12x2 + -1(88x) = 0 Multiply -1 * 12 120 + -12x2 + -1(88x) = 0 Remove parenthesis around (88x) 120 + -12x2 + -1 * 88x = 0 Multiply -1 * 88 120 + -12x2 + -88x = 0 Reorder the terms: 120 + -88x + -12x2 = 0 Solving 120 + -88x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -22x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + -22x + -3x2)' equal to zero and attempt to solve: Simplifying 30 + -22x + -3x2 = 0 Solving 30 + -22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 7.333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 7.333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7.333333333x + x2 = 0 + 10 7.333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 7.333333333x + x2 = 10 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 10 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 10 + 13.44444445 Combine like terms: 10 + 13.44444445 = 23.44444445 13.44444445 + 7.333333333x + x2 = 23.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 23.44444445 Calculate the square root of the right side: 4.841946349 Break this problem into two subproblems by setting (x + 3.666666667) equal to 4.841946349 and -4.841946349.Subproblem 1
x + 3.666666667 = 4.841946349 Simplifying x + 3.666666667 = 4.841946349 Reorder the terms: 3.666666667 + x = 4.841946349 Solving 3.666666667 + x = 4.841946349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 4.841946349 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 4.841946349 + -3.666666667 x = 4.841946349 + -3.666666667 Combine like terms: 4.841946349 + -3.666666667 = 1.175279682 x = 1.175279682 Simplifying x = 1.175279682Subproblem 2
x + 3.666666667 = -4.841946349 Simplifying x + 3.666666667 = -4.841946349 Reorder the terms: 3.666666667 + x = -4.841946349 Solving 3.666666667 + x = -4.841946349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -4.841946349 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -4.841946349 + -3.666666667 x = -4.841946349 + -3.666666667 Combine like terms: -4.841946349 + -3.666666667 = -8.508613016 x = -8.508613016 Simplifying x = -8.508613016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.175279682, -8.508613016}Solution
x = {1.175279682, -8.508613016}
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