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Simplifying 0.06x2 = 2.4x + 0.6 Reorder the terms: 0.06x2 = 0.6 + 2.4x Solving 0.06x2 = 0.6 + 2.4x Solving for variable 'x'. Reorder the terms: -0.6 + -2.4x + 0.06x2 = 0.6 + 2.4x + -0.6 + -2.4x Reorder the terms: -0.6 + -2.4x + 0.06x2 = 0.6 + -0.6 + 2.4x + -2.4x Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + -2.4x + 0.06x2 = 0.0 + 2.4x + -2.4x -0.6 + -2.4x + 0.06x2 = 2.4x + -2.4x Combine like terms: 2.4x + -2.4x = 0.0 -0.6 + -2.4x + 0.06x2 = 0.0 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -10 + -40x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -40x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -40x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -40x + x2 = 0 + 10 -40x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -40x + x2 = 10 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 10 + 400 Reorder the terms: 400 + -40x + x2 = 10 + 400 Combine like terms: 10 + 400 = 410 400 + -40x + x2 = 410 Factor a perfect square on the left side: (x + -20)(x + -20) = 410 Calculate the square root of the right side: 20.248456731 Break this problem into two subproblems by setting (x + -20) equal to 20.248456731 and -20.248456731.Subproblem 1
x + -20 = 20.248456731 Simplifying x + -20 = 20.248456731 Reorder the terms: -20 + x = 20.248456731 Solving -20 + x = 20.248456731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.248456731 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.248456731 + 20 x = 20.248456731 + 20 Combine like terms: 20.248456731 + 20 = 40.248456731 x = 40.248456731 Simplifying x = 40.248456731Subproblem 2
x + -20 = -20.248456731 Simplifying x + -20 = -20.248456731 Reorder the terms: -20 + x = -20.248456731 Solving -20 + x = -20.248456731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.248456731 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.248456731 + 20 x = -20.248456731 + 20 Combine like terms: -20.248456731 + 20 = -0.248456731 x = -0.248456731 Simplifying x = -0.248456731Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.248456731, -0.248456731}
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