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Simplifying 5x(2x + 0.02) = 67 Reorder the terms: 5x(0.02 + 2x) = 67 (0.02 * 5x + 2x * 5x) = 67 (0.1x + 10x2) = 67 Solving 0.1x + 10x2 = 67 Solving for variable 'x'. Reorder the terms: -67 + 0.1x + 10x2 = 67 + -67 Combine like terms: 67 + -67 = 0 -67 + 0.1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.7 + 0.01x + x2 = 0.0 Move the constant term to the right: Add '6.7' to each side of the equation. -6.7 + 0.01x + 6.7 + x2 = 0.0 + 6.7 Reorder the terms: -6.7 + 6.7 + 0.01x + x2 = 0.0 + 6.7 Combine like terms: -6.7 + 6.7 = 0.0 0.0 + 0.01x + x2 = 0.0 + 6.7 0.01x + x2 = 0.0 + 6.7 Combine like terms: 0.0 + 6.7 = 6.7 0.01x + x2 = 6.7 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 = 6.7 + 0.000025 Reorder the terms: 0.000025 + 0.01x + x2 = 6.7 + 0.000025 Combine like terms: 6.7 + 0.000025 = 6.700025 0.000025 + 0.01x + x2 = 6.700025 Factor a perfect square on the left side: (x + 0.005)(x + 0.005) = 6.700025 Calculate the square root of the right side: 2.58844065 Break this problem into two subproblems by setting (x + 0.005) equal to 2.58844065 and -2.58844065.Subproblem 1
x + 0.005 = 2.58844065 Simplifying x + 0.005 = 2.58844065 Reorder the terms: 0.005 + x = 2.58844065 Solving 0.005 + x = 2.58844065 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 = 2.58844065 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = 2.58844065 + -0.005 x = 2.58844065 + -0.005 Combine like terms: 2.58844065 + -0.005 = 2.58344065 x = 2.58344065 Simplifying x = 2.58344065Subproblem 2
x + 0.005 = -2.58844065 Simplifying x + 0.005 = -2.58844065 Reorder the terms: 0.005 + x = -2.58844065 Solving 0.005 + x = -2.58844065 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 = -2.58844065 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + x = -2.58844065 + -0.005 x = -2.58844065 + -0.005 Combine like terms: -2.58844065 + -0.005 = -2.59344065 x = -2.59344065 Simplifying x = -2.59344065Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.58344065, -2.59344065}
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