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Simplifying 0.02 = (x2 * 2) + -1(x * 0.02) Reorder the terms for easier multiplication: 0.02 = (2x2) + -1(x * 0.02) Reorder the terms for easier multiplication: 0.02 = (2x2) + -1(0.02x) Remove parenthesis around (0.02x) 0.02 = (2x2) + -1 * 0.02x Multiply -1 * 0.02 0.02 = (2x2) + -0.02x Reorder the terms: 0.02 = -0.02x + (2x2) Solving 0.02 = -0.02x + (2x2) Solving for variable 'x'. Reorder the terms: 0.02 + 0.02x + (-2x2) = -0.02x + 0.02x + (2x2) + (-2x2) Combine like terms: -0.02x + 0.02x = 0.00 0.02 + 0.02x + (-2x2) = 0.00 + (2x2) + (-2x2) 0.02 + 0.02x + (-2x2) = (2x2) + (-2x2) Combine like terms: (2x2) + (-2x2) = 0 0.02 + 0.02x + (-2x2) = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.01 + -0.01x + x2 = 0 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + -0.01x + 0.01 + x2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + -0.01x + x2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + -0.01x + x2 = 0 + 0.01 -0.01x + x2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 -0.01x + x2 = 0.01 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 = 0.01 + 0.000025 Reorder the terms: 0.000025 + -0.01x + x2 = 0.01 + 0.000025 Combine like terms: 0.01 + 0.000025 = 0.010025 0.000025 + -0.01x + x2 = 0.010025 Factor a perfect square on the left side: ((x) + -0.005)((x) + -0.005) = 0.010025 Calculate the square root of the right side: 0.100124922 Break this problem into two subproblems by setting ((x) + -0.005) equal to 0.100124922 and -0.100124922.Subproblem 1
(x) + -0.005 = 0.100124922 Simplifying (x) + -0.005 = 0.100124922 x + -0.005 = 0.100124922 Reorder the terms: -0.005 + x = 0.100124922 Solving -0.005 + x = 0.100124922 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 = 0.100124922 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = 0.100124922 + 0.005 x = 0.100124922 + 0.005 Combine like terms: 0.100124922 + 0.005 = 0.105124922 x = 0.105124922 Simplifying x = 0.105124922Subproblem 2
(x) + -0.005 = -0.100124922 Simplifying (x) + -0.005 = -0.100124922 x + -0.005 = -0.100124922 Reorder the terms: -0.005 + x = -0.100124922 Solving -0.005 + x = -0.100124922 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 = -0.100124922 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = -0.100124922 + 0.005 x = -0.100124922 + 0.005 Combine like terms: -0.100124922 + 0.005 = -0.095124922 x = -0.095124922 Simplifying x = -0.095124922Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.105124922, -0.095124922}
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