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Simplifying 70x2 + 140x + -130 = 0 Reorder the terms: -130 + 140x + 70x2 = 0 Solving -130 + 140x + 70x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-13 + 14x + 7x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-13 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying -13 + 14x + 7x2 = 0 Solving -13 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 2x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 2x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 2x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.857142857 2x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 2x + x2 = 1.857142857 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.857142857 + 1 Reorder the terms: 1 + 2x + x2 = 1.857142857 + 1 Combine like terms: 1.857142857 + 1 = 2.857142857 1 + 2x + x2 = 2.857142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.857142857 Calculate the square root of the right side: 1.690308509 Break this problem into two subproblems by setting (x + 1) equal to 1.690308509 and -1.690308509.Subproblem 1
x + 1 = 1.690308509 Simplifying x + 1 = 1.690308509 Reorder the terms: 1 + x = 1.690308509 Solving 1 + x = 1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.690308509 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.690308509 + -1 x = 1.690308509 + -1 Combine like terms: 1.690308509 + -1 = 0.690308509 x = 0.690308509 Simplifying x = 0.690308509Subproblem 2
x + 1 = -1.690308509 Simplifying x + 1 = -1.690308509 Reorder the terms: 1 + x = -1.690308509 Solving 1 + x = -1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.690308509 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.690308509 + -1 x = -1.690308509 + -1 Combine like terms: -1.690308509 + -1 = -2.690308509 x = -2.690308509 Simplifying x = -2.690308509Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.690308509, -2.690308509}Solution
x = {0.690308509, -2.690308509}
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