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Simplifying 150 + -100x + 12x2 = 0 Solving 150 + -100x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -50x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -50x + 6x2)' equal to zero and attempt to solve: Simplifying 75 + -50x + 6x2 = 0 Solving 75 + -50x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 12.5 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -8.333333333x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -8.333333333x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -8.333333333x + x2 = 0 + -12.5 -8.333333333x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -8.333333333x + x2 = -12.5 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = -12.5 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -12.5 + 17.36111111 Combine like terms: -12.5 + 17.36111111 = 4.86111111 17.36111111 + -8.333333333x + x2 = 4.86111111 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 4.86111111 Calculate the square root of the right side: 2.204792759 Break this problem into two subproblems by setting (x + -4.166666667) equal to 2.204792759 and -2.204792759.Subproblem 1
x + -4.166666667 = 2.204792759 Simplifying x + -4.166666667 = 2.204792759 Reorder the terms: -4.166666667 + x = 2.204792759 Solving -4.166666667 + x = 2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 2.204792759 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 2.204792759 + 4.166666667 x = 2.204792759 + 4.166666667 Combine like terms: 2.204792759 + 4.166666667 = 6.371459426 x = 6.371459426 Simplifying x = 6.371459426Subproblem 2
x + -4.166666667 = -2.204792759 Simplifying x + -4.166666667 = -2.204792759 Reorder the terms: -4.166666667 + x = -2.204792759 Solving -4.166666667 + x = -2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -2.204792759 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -2.204792759 + 4.166666667 x = -2.204792759 + 4.166666667 Combine like terms: -2.204792759 + 4.166666667 = 1.961873908 x = 1.961873908 Simplifying x = 1.961873908Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.371459426, 1.961873908}Solution
x = {6.371459426, 1.961873908}
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