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Simplifying 400x + -2000x2 + 10 = 0 Reorder the terms: 10 + 400x + -2000x2 = 0 Solving 10 + 400x + -2000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(1 + 40x + -200x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1 + 40x + -200x2)' equal to zero and attempt to solve: Simplifying 1 + 40x + -200x2 = 0 Solving 1 + 40x + -200x2 = 0 Begin completing the square. Divide all terms by -200 the coefficient of the squared term: Divide each side by '-200'. -0.005 + -0.2x + x2 = 0.00 Move the constant term to the right: Add '0.005' to each side of the equation. -0.005 + -0.2x + 0.005 + x2 = 0.00 + 0.005 Reorder the terms: -0.005 + 0.005 + -0.2x + x2 = 0.00 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + -0.2x + x2 = 0.00 + 0.005 -0.2x + x2 = 0.00 + 0.005 Combine like terms: 0.00 + 0.005 = 0.005 -0.2x + x2 = 0.005 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.005 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.005 + 0.01 Combine like terms: 0.005 + 0.01 = 0.015 0.01 + -0.2x + x2 = 0.015 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.015 Calculate the square root of the right side: 0.122474487 Break this problem into two subproblems by setting (x + -0.1) equal to 0.122474487 and -0.122474487.Subproblem 1
x + -0.1 = 0.122474487 Simplifying x + -0.1 = 0.122474487 Reorder the terms: -0.1 + x = 0.122474487 Solving -0.1 + x = 0.122474487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.122474487 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.122474487 + 0.1 x = 0.122474487 + 0.1 Combine like terms: 0.122474487 + 0.1 = 0.222474487 x = 0.222474487 Simplifying x = 0.222474487Subproblem 2
x + -0.1 = -0.122474487 Simplifying x + -0.1 = -0.122474487 Reorder the terms: -0.1 + x = -0.122474487 Solving -0.1 + x = -0.122474487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.122474487 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.122474487 + 0.1 x = -0.122474487 + 0.1 Combine like terms: -0.122474487 + 0.1 = -0.022474487 x = -0.022474487 Simplifying x = -0.022474487Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.222474487, -0.022474487}Solution
x = {0.222474487, -0.022474487}
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