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Simplifying 3x2 + -84x + 588 = 42 Reorder the terms: 588 + -84x + 3x2 = 42 Solving 588 + -84x + 3x2 = 42 Solving for variable 'x'. Reorder the terms: 588 + -42 + -84x + 3x2 = 42 + -42 Combine like terms: 588 + -42 = 546 546 + -84x + 3x2 = 42 + -42 Combine like terms: 42 + -42 = 0 546 + -84x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(182 + -28x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(182 + -28x + x2)' equal to zero and attempt to solve: Simplifying 182 + -28x + x2 = 0 Solving 182 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-182' to each side of the equation. 182 + -28x + -182 + x2 = 0 + -182 Reorder the terms: 182 + -182 + -28x + x2 = 0 + -182 Combine like terms: 182 + -182 = 0 0 + -28x + x2 = 0 + -182 -28x + x2 = 0 + -182 Combine like terms: 0 + -182 = -182 -28x + x2 = -182 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -182 + 196 Reorder the terms: 196 + -28x + x2 = -182 + 196 Combine like terms: -182 + 196 = 14 196 + -28x + x2 = 14 Factor a perfect square on the left side: (x + -14)(x + -14) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -14) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -14 = 3.741657387 Simplifying x + -14 = 3.741657387 Reorder the terms: -14 + x = 3.741657387 Solving -14 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 3.741657387 + 14 Combine like terms: -14 + 14 = 0 0 + x = 3.741657387 + 14 x = 3.741657387 + 14 Combine like terms: 3.741657387 + 14 = 17.741657387 x = 17.741657387 Simplifying x = 17.741657387Subproblem 2
x + -14 = -3.741657387 Simplifying x + -14 = -3.741657387 Reorder the terms: -14 + x = -3.741657387 Solving -14 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -3.741657387 + 14 Combine like terms: -14 + 14 = 0 0 + x = -3.741657387 + 14 x = -3.741657387 + 14 Combine like terms: -3.741657387 + 14 = 10.258342613 x = 10.258342613 Simplifying x = 10.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.741657387, 10.258342613}Solution
x = {17.741657387, 10.258342613}
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