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Simplifying -100x2 + 1x + 26 = 0 Reorder the terms: 26 + 1x + -100x2 = 0 Solving 26 + 1x + -100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -100 the coefficient of the squared term: Divide each side by '-100'. -0.26 + -0.01x + x2 = 0 Move the constant term to the right: Add '0.26' to each side of the equation. -0.26 + -0.01x + 0.26 + x2 = 0 + 0.26 Reorder the terms: -0.26 + 0.26 + -0.01x + x2 = 0 + 0.26 Combine like terms: -0.26 + 0.26 = 0.00 0.00 + -0.01x + x2 = 0 + 0.26 -0.01x + x2 = 0 + 0.26 Combine like terms: 0 + 0.26 = 0.26 -0.01x + x2 = 0.26 The x term is -0.01x. Take half its coefficient (-0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. -0.01x + 0.000025 + x2 = 0.26 + 0.000025 Reorder the terms: 0.000025 + -0.01x + x2 = 0.26 + 0.000025 Combine like terms: 0.26 + 0.000025 = 0.260025 0.000025 + -0.01x + x2 = 0.260025 Factor a perfect square on the left side: (x + -0.005)(x + -0.005) = 0.260025 Calculate the square root of the right side: 0.509926465 Break this problem into two subproblems by setting (x + -0.005) equal to 0.509926465 and -0.509926465.Subproblem 1
x + -0.005 = 0.509926465 Simplifying x + -0.005 = 0.509926465 Reorder the terms: -0.005 + x = 0.509926465 Solving -0.005 + x = 0.509926465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = 0.509926465 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = 0.509926465 + 0.005 x = 0.509926465 + 0.005 Combine like terms: 0.509926465 + 0.005 = 0.514926465 x = 0.514926465 Simplifying x = 0.514926465Subproblem 2
x + -0.005 = -0.509926465 Simplifying x + -0.005 = -0.509926465 Reorder the terms: -0.005 + x = -0.509926465 Solving -0.005 + x = -0.509926465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = -0.509926465 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = -0.509926465 + 0.005 x = -0.509926465 + 0.005 Combine like terms: -0.509926465 + 0.005 = -0.504926465 x = -0.504926465 Simplifying x = -0.504926465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.514926465, -0.504926465}
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