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Simplifying 34x + -8 + 34x * 5x + 12 = 12 Reorder the terms for easier multiplication: 34x + -8 + 34 * 5x * x + 12 = 12 Multiply 34 * 5 34x + -8 + 170x * x + 12 = 12 Multiply x * x 34x + -8 + 170x2 + 12 = 12 Reorder the terms: -8 + 12 + 34x + 170x2 = 12 Combine like terms: -8 + 12 = 4 4 + 34x + 170x2 = 12 Solving 4 + 34x + 170x2 = 12 Solving for variable 'x'. Reorder the terms: 4 + -12 + 34x + 170x2 = 12 + -12 Combine like terms: 4 + -12 = -8 -8 + 34x + 170x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -8 + 34x + 170x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 17x + 85x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 17x + 85x2)' equal to zero and attempt to solve: Simplifying -4 + 17x + 85x2 = 0 Solving -4 + 17x + 85x2 = 0 Begin completing the square. Divide all terms by 85 the coefficient of the squared term: Divide each side by '85'. -0.04705882353 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.04705882353' to each side of the equation. -0.04705882353 + 0.2x + 0.04705882353 + x2 = 0 + 0.04705882353 Reorder the terms: -0.04705882353 + 0.04705882353 + 0.2x + x2 = 0 + 0.04705882353 Combine like terms: -0.04705882353 + 0.04705882353 = 0.00000000000 0.00000000000 + 0.2x + x2 = 0 + 0.04705882353 0.2x + x2 = 0 + 0.04705882353 Combine like terms: 0 + 0.04705882353 = 0.04705882353 0.2x + x2 = 0.04705882353 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.04705882353 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.04705882353 + 0.01 Combine like terms: 0.04705882353 + 0.01 = 0.05705882353 0.01 + 0.2x + x2 = 0.05705882353 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.05705882353 Calculate the square root of the right side: 0.238869888 Break this problem into two subproblems by setting (x + 0.1) equal to 0.238869888 and -0.238869888.Subproblem 1
x + 0.1 = 0.238869888 Simplifying x + 0.1 = 0.238869888 Reorder the terms: 0.1 + x = 0.238869888 Solving 0.1 + x = 0.238869888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.238869888 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.238869888 + -0.1 x = 0.238869888 + -0.1 Combine like terms: 0.238869888 + -0.1 = 0.138869888 x = 0.138869888 Simplifying x = 0.138869888Subproblem 2
x + 0.1 = -0.238869888 Simplifying x + 0.1 = -0.238869888 Reorder the terms: 0.1 + x = -0.238869888 Solving 0.1 + x = -0.238869888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.238869888 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.238869888 + -0.1 x = -0.238869888 + -0.1 Combine like terms: -0.238869888 + -0.1 = -0.338869888 x = -0.338869888 Simplifying x = -0.338869888Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.138869888, -0.338869888}Solution
x = {0.138869888, -0.338869888}
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