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Simplifying 3400x2 + 20x + -4 = 0 Reorder the terms: -4 + 20x + 3400x2 = 0 Solving -4 + 20x + 3400x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 5x + 850x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 5x + 850x2)' equal to zero and attempt to solve: Simplifying -1 + 5x + 850x2 = 0 Solving -1 + 5x + 850x2 = 0 Begin completing the square. Divide all terms by 850 the coefficient of the squared term: Divide each side by '850'. -0.001176470588 + 0.005882352941x + x2 = 0.0 Move the constant term to the right: Add '0.001176470588' to each side of the equation. -0.001176470588 + 0.005882352941x + 0.001176470588 + x2 = 0.0 + 0.001176470588 Reorder the terms: -0.001176470588 + 0.001176470588 + 0.005882352941x + x2 = 0.0 + 0.001176470588 Combine like terms: -0.001176470588 + 0.001176470588 = 0.000000000000 0.000000000000 + 0.005882352941x + x2 = 0.0 + 0.001176470588 0.005882352941x + x2 = 0.0 + 0.001176470588 Combine like terms: 0.0 + 0.001176470588 = 0.001176470588 0.005882352941x + x2 = 0.001176470588 The x term is 0.005882352941x. Take half its coefficient (0.002941176471). Square it (0.000008650519034) and add it to both sides. Add '0.000008650519034' to each side of the equation. 0.005882352941x + 0.000008650519034 + x2 = 0.001176470588 + 0.000008650519034 Reorder the terms: 0.000008650519034 + 0.005882352941x + x2 = 0.001176470588 + 0.000008650519034 Combine like terms: 0.001176470588 + 0.000008650519034 = 0.001185121107034 0.000008650519034 + 0.005882352941x + x2 = 0.001185121107034 Factor a perfect square on the left side: (x + 0.002941176471)(x + 0.002941176471) = 0.001185121107034 Calculate the square root of the right side: 0.034425588 Break this problem into two subproblems by setting (x + 0.002941176471) equal to 0.034425588 and -0.034425588.Subproblem 1
x + 0.002941176471 = 0.034425588 Simplifying x + 0.002941176471 = 0.034425588 Reorder the terms: 0.002941176471 + x = 0.034425588 Solving 0.002941176471 + x = 0.034425588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.002941176471' to each side of the equation. 0.002941176471 + -0.002941176471 + x = 0.034425588 + -0.002941176471 Combine like terms: 0.002941176471 + -0.002941176471 = 0.000000000000 0.000000000000 + x = 0.034425588 + -0.002941176471 x = 0.034425588 + -0.002941176471 Combine like terms: 0.034425588 + -0.002941176471 = 0.031484411529 x = 0.031484411529 Simplifying x = 0.031484411529Subproblem 2
x + 0.002941176471 = -0.034425588 Simplifying x + 0.002941176471 = -0.034425588 Reorder the terms: 0.002941176471 + x = -0.034425588 Solving 0.002941176471 + x = -0.034425588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.002941176471' to each side of the equation. 0.002941176471 + -0.002941176471 + x = -0.034425588 + -0.002941176471 Combine like terms: 0.002941176471 + -0.002941176471 = 0.000000000000 0.000000000000 + x = -0.034425588 + -0.002941176471 x = -0.034425588 + -0.002941176471 Combine like terms: -0.034425588 + -0.002941176471 = -0.037366764471 x = -0.037366764471 Simplifying x = -0.037366764471Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.031484411529, -0.037366764471}Solution
x = {0.031484411529, -0.037366764471}
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