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Simplifying 700x2 + 100x + -16 = 0 Reorder the terms: -16 + 100x + 700x2 = 0 Solving -16 + 100x + 700x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 25x + 175x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 25x + 175x2)' equal to zero and attempt to solve: Simplifying -4 + 25x + 175x2 = 0 Solving -4 + 25x + 175x2 = 0 Begin completing the square. Divide all terms by 175 the coefficient of the squared term: Divide each side by '175'. -0.02285714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.02285714286' to each side of the equation. -0.02285714286 + 0.1428571429x + 0.02285714286 + x2 = 0 + 0.02285714286 Reorder the terms: -0.02285714286 + 0.02285714286 + 0.1428571429x + x2 = 0 + 0.02285714286 Combine like terms: -0.02285714286 + 0.02285714286 = 0.00000000000 0.00000000000 + 0.1428571429x + x2 = 0 + 0.02285714286 0.1428571429x + x2 = 0 + 0.02285714286 Combine like terms: 0 + 0.02285714286 = 0.02285714286 0.1428571429x + x2 = 0.02285714286 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 0.02285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 0.02285714286 + 0.005102040819 Combine like terms: 0.02285714286 + 0.005102040819 = 0.027959183679 0.005102040819 + 0.1428571429x + x2 = 0.027959183679 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 0.027959183679 Calculate the square root of the right side: 0.167209999 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 0.167209999 and -0.167209999.Subproblem 1
x + 0.07142857145 = 0.167209999 Simplifying x + 0.07142857145 = 0.167209999 Reorder the terms: 0.07142857145 + x = 0.167209999 Solving 0.07142857145 + x = 0.167209999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 0.167209999 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 0.167209999 + -0.07142857145 x = 0.167209999 + -0.07142857145 Combine like terms: 0.167209999 + -0.07142857145 = 0.09578142755 x = 0.09578142755 Simplifying x = 0.09578142755Subproblem 2
x + 0.07142857145 = -0.167209999 Simplifying x + 0.07142857145 = -0.167209999 Reorder the terms: 0.07142857145 + x = -0.167209999 Solving 0.07142857145 + x = -0.167209999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -0.167209999 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -0.167209999 + -0.07142857145 x = -0.167209999 + -0.07142857145 Combine like terms: -0.167209999 + -0.07142857145 = -0.23863857045 x = -0.23863857045 Simplifying x = -0.23863857045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.09578142755, -0.23863857045}Solution
x = {0.09578142755, -0.23863857045}
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