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Simplifying 700x2 + 8x + -130 = 0 Reorder the terms: -130 + 8x + 700x2 = 0 Solving -130 + 8x + 700x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 4x + 350x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 4x + 350x2)' equal to zero and attempt to solve: Simplifying -65 + 4x + 350x2 = 0 Solving -65 + 4x + 350x2 = 0 Begin completing the square. Divide all terms by 350 the coefficient of the squared term: Divide each side by '350'. -0.1857142857 + 0.01142857143x + x2 = 0.0 Move the constant term to the right: Add '0.1857142857' to each side of the equation. -0.1857142857 + 0.01142857143x + 0.1857142857 + x2 = 0.0 + 0.1857142857 Reorder the terms: -0.1857142857 + 0.1857142857 + 0.01142857143x + x2 = 0.0 + 0.1857142857 Combine like terms: -0.1857142857 + 0.1857142857 = 0.0000000000 0.0000000000 + 0.01142857143x + x2 = 0.0 + 0.1857142857 0.01142857143x + x2 = 0.0 + 0.1857142857 Combine like terms: 0.0 + 0.1857142857 = 0.1857142857 0.01142857143x + x2 = 0.1857142857 The x term is 0.01142857143x. Take half its coefficient (0.005714285715). Square it (0.00003265306123) and add it to both sides. Add '0.00003265306123' to each side of the equation. 0.01142857143x + 0.00003265306123 + x2 = 0.1857142857 + 0.00003265306123 Reorder the terms: 0.00003265306123 + 0.01142857143x + x2 = 0.1857142857 + 0.00003265306123 Combine like terms: 0.1857142857 + 0.00003265306123 = 0.18574693876123 0.00003265306123 + 0.01142857143x + x2 = 0.18574693876123 Factor a perfect square on the left side: (x + 0.005714285715)(x + 0.005714285715) = 0.18574693876123 Calculate the square root of the right side: 0.430983687 Break this problem into two subproblems by setting (x + 0.005714285715) equal to 0.430983687 and -0.430983687.Subproblem 1
x + 0.005714285715 = 0.430983687 Simplifying x + 0.005714285715 = 0.430983687 Reorder the terms: 0.005714285715 + x = 0.430983687 Solving 0.005714285715 + x = 0.430983687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005714285715' to each side of the equation. 0.005714285715 + -0.005714285715 + x = 0.430983687 + -0.005714285715 Combine like terms: 0.005714285715 + -0.005714285715 = 0.000000000000 0.000000000000 + x = 0.430983687 + -0.005714285715 x = 0.430983687 + -0.005714285715 Combine like terms: 0.430983687 + -0.005714285715 = 0.425269401285 x = 0.425269401285 Simplifying x = 0.425269401285Subproblem 2
x + 0.005714285715 = -0.430983687 Simplifying x + 0.005714285715 = -0.430983687 Reorder the terms: 0.005714285715 + x = -0.430983687 Solving 0.005714285715 + x = -0.430983687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.005714285715' to each side of the equation. 0.005714285715 + -0.005714285715 + x = -0.430983687 + -0.005714285715 Combine like terms: 0.005714285715 + -0.005714285715 = 0.000000000000 0.000000000000 + x = -0.430983687 + -0.005714285715 x = -0.430983687 + -0.005714285715 Combine like terms: -0.430983687 + -0.005714285715 = -0.436697972715 x = -0.436697972715 Simplifying x = -0.436697972715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425269401285, -0.436697972715}Solution
x = {0.425269401285, -0.436697972715}
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