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Simplifying 4200 = 10x2 + -94x + 3900 Reorder the terms: 4200 = 3900 + -94x + 10x2 Solving 4200 = 3900 + -94x + 10x2 Solving for variable 'x'. Combine like terms: 4200 + -3900 = 300 300 + 94x + -10x2 = 3900 + -94x + 10x2 + -3900 + 94x + -10x2 Reorder the terms: 300 + 94x + -10x2 = 3900 + -3900 + -94x + 94x + 10x2 + -10x2 Combine like terms: 3900 + -3900 = 0 300 + 94x + -10x2 = 0 + -94x + 94x + 10x2 + -10x2 300 + 94x + -10x2 = -94x + 94x + 10x2 + -10x2 Combine like terms: -94x + 94x = 0 300 + 94x + -10x2 = 0 + 10x2 + -10x2 300 + 94x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 300 + 94x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(150 + 47x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(150 + 47x + -5x2)' equal to zero and attempt to solve: Simplifying 150 + 47x + -5x2 = 0 Solving 150 + 47x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -30 + -9.4x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -9.4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -9.4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -9.4x + x2 = 0 + 30 -9.4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -9.4x + x2 = 30 The x term is -9.4x. Take half its coefficient (-4.7). Square it (22.09) and add it to both sides. Add '22.09' to each side of the equation. -9.4x + 22.09 + x2 = 30 + 22.09 Reorder the terms: 22.09 + -9.4x + x2 = 30 + 22.09 Combine like terms: 30 + 22.09 = 52.09 22.09 + -9.4x + x2 = 52.09 Factor a perfect square on the left side: (x + -4.7)(x + -4.7) = 52.09 Calculate the square root of the right side: 7.21734023 Break this problem into two subproblems by setting (x + -4.7) equal to 7.21734023 and -7.21734023.Subproblem 1
x + -4.7 = 7.21734023 Simplifying x + -4.7 = 7.21734023 Reorder the terms: -4.7 + x = 7.21734023 Solving -4.7 + x = 7.21734023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + x = 7.21734023 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + x = 7.21734023 + 4.7 x = 7.21734023 + 4.7 Combine like terms: 7.21734023 + 4.7 = 11.91734023 x = 11.91734023 Simplifying x = 11.91734023Subproblem 2
x + -4.7 = -7.21734023 Simplifying x + -4.7 = -7.21734023 Reorder the terms: -4.7 + x = -7.21734023 Solving -4.7 + x = -7.21734023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + x = -7.21734023 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + x = -7.21734023 + 4.7 x = -7.21734023 + 4.7 Combine like terms: -7.21734023 + 4.7 = -2.51734023 x = -2.51734023 Simplifying x = -2.51734023Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.91734023, -2.51734023}Solution
x = {11.91734023, -2.51734023}
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