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Simplifying -12x2 + -176x + 3200 = 0 Reorder the terms: 3200 + -176x + -12x2 = 0 Solving 3200 + -176x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(800 + -44x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(800 + -44x + -3x2)' equal to zero and attempt to solve: Simplifying 800 + -44x + -3x2 = 0 Solving 800 + -44x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -266.6666667 + 14.66666667x + x2 = 0 Move the constant term to the right: Add '266.6666667' to each side of the equation. -266.6666667 + 14.66666667x + 266.6666667 + x2 = 0 + 266.6666667 Reorder the terms: -266.6666667 + 266.6666667 + 14.66666667x + x2 = 0 + 266.6666667 Combine like terms: -266.6666667 + 266.6666667 = 0.0000000 0.0000000 + 14.66666667x + x2 = 0 + 266.6666667 14.66666667x + x2 = 0 + 266.6666667 Combine like terms: 0 + 266.6666667 = 266.6666667 14.66666667x + x2 = 266.6666667 The x term is 14.66666667x. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667x + 53.77777780 + x2 = 266.6666667 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667x + x2 = 266.6666667 + 53.77777780 Combine like terms: 266.6666667 + 53.77777780 = 320.4444445 53.77777780 + 14.66666667x + x2 = 320.4444445 Factor a perfect square on the left side: (x + 7.333333335)(x + 7.333333335) = 320.4444445 Calculate the square root of the right side: 17.900962111 Break this problem into two subproblems by setting (x + 7.333333335) equal to 17.900962111 and -17.900962111.Subproblem 1
x + 7.333333335 = 17.900962111 Simplifying x + 7.333333335 = 17.900962111 Reorder the terms: 7.333333335 + x = 17.900962111 Solving 7.333333335 + x = 17.900962111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = 17.900962111 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = 17.900962111 + -7.333333335 x = 17.900962111 + -7.333333335 Combine like terms: 17.900962111 + -7.333333335 = 10.567628776 x = 10.567628776 Simplifying x = 10.567628776Subproblem 2
x + 7.333333335 = -17.900962111 Simplifying x + 7.333333335 = -17.900962111 Reorder the terms: 7.333333335 + x = -17.900962111 Solving 7.333333335 + x = -17.900962111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = -17.900962111 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = -17.900962111 + -7.333333335 x = -17.900962111 + -7.333333335 Combine like terms: -17.900962111 + -7.333333335 = -25.234295446 x = -25.234295446 Simplifying x = -25.234295446Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.567628776, -25.234295446}Solution
x = {10.567628776, -25.234295446}
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