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Simplifying 10 = -0.2x2 + 3x + 6 Reorder the terms: 10 = 6 + 3x + -0.2x2 Solving 10 = 6 + 3x + -0.2x2 Solving for variable 'x'. Combine like terms: 10 + -6 = 4 4 + -3x + 0.2x2 = 6 + 3x + -0.2x2 + -6 + -3x + 0.2x2 Reorder the terms: 4 + -3x + 0.2x2 = 6 + -6 + 3x + -3x + -0.2x2 + 0.2x2 Combine like terms: 6 + -6 = 0 4 + -3x + 0.2x2 = 0 + 3x + -3x + -0.2x2 + 0.2x2 4 + -3x + 0.2x2 = 3x + -3x + -0.2x2 + 0.2x2 Combine like terms: 3x + -3x = 0 4 + -3x + 0.2x2 = 0 + -0.2x2 + 0.2x2 4 + -3x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 4 + -3x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 20 + -15x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -15x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -15x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -15x + x2 = 0 + -20 -15x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -15x + x2 = -20 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -20 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -20 + 56.25 Combine like terms: -20 + 56.25 = 36.25 56.25 + -15x + x2 = 36.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -7.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -7.5 = 6.020797289 Simplifying x + -7.5 = 6.020797289 Reorder the terms: -7.5 + x = 6.020797289 Solving -7.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.020797289 + 7.5 x = 6.020797289 + 7.5 Combine like terms: 6.020797289 + 7.5 = 13.520797289 x = 13.520797289 Simplifying x = 13.520797289Subproblem 2
x + -7.5 = -6.020797289 Simplifying x + -7.5 = -6.020797289 Reorder the terms: -7.5 + x = -6.020797289 Solving -7.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.020797289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.020797289 + 7.5 x = -6.020797289 + 7.5 Combine like terms: -6.020797289 + 7.5 = 1.479202711 x = 1.479202711 Simplifying x = 1.479202711Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.520797289, 1.479202711}
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