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Simplifying 0.20(45 + -1x) = x2 (45 * 0.20 + -1x * 0.20) = x2 (9 + -0.2x) = x2 Solving 9 + -0.2x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 9 + -0.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 0.2x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.2x + x2 = 0 + 9 0.2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.2x + x2 = 9 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 = 9 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 9 + 0.01 Combine like terms: 9 + 0.01 = 9.01 0.01 + 0.2x + x2 = 9.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 9.01 Calculate the square root of the right side: 3.001666204 Break this problem into two subproblems by setting (x + 0.1) equal to 3.001666204 and -3.001666204.Subproblem 1
x + 0.1 = 3.001666204 Simplifying x + 0.1 = 3.001666204 Reorder the terms: 0.1 + x = 3.001666204 Solving 0.1 + x = 3.001666204 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 = 3.001666204 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 3.001666204 + -0.1 x = 3.001666204 + -0.1 Combine like terms: 3.001666204 + -0.1 = 2.901666204 x = 2.901666204 Simplifying x = 2.901666204Subproblem 2
x + 0.1 = -3.001666204 Simplifying x + 0.1 = -3.001666204 Reorder the terms: 0.1 + x = -3.001666204 Solving 0.1 + x = -3.001666204 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 = -3.001666204 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -3.001666204 + -0.1 x = -3.001666204 + -0.1 Combine like terms: -3.001666204 + -0.1 = -3.101666204 x = -3.101666204 Simplifying x = -3.101666204Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.901666204, -3.101666204}
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