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Simplifying 10 = 0.2x2 + 3x + 2 Reorder the terms: 10 = 2 + 3x + 0.2x2 Solving 10 = 2 + 3x + 0.2x2 Solving for variable 'x'. Combine like terms: 10 + -2 = 8 8 + -3x + -0.2x2 = 2 + 3x + 0.2x2 + -2 + -3x + -0.2x2 Reorder the terms: 8 + -3x + -0.2x2 = 2 + -2 + 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: 2 + -2 = 0 8 + -3x + -0.2x2 = 0 + 3x + -3x + 0.2x2 + -0.2x2 8 + -3x + -0.2x2 = 3x + -3x + 0.2x2 + -0.2x2 Combine like terms: 3x + -3x = 0 8 + -3x + -0.2x2 = 0 + 0.2x2 + -0.2x2 8 + -3x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 8 + -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'. -40 + 15x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 15x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 15x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 15x + x2 = 0 + 40 15x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 15x + x2 = 40 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 = 40 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 40 + 56.25 Combine like terms: 40 + 56.25 = 96.25 56.25 + 15x + x2 = 96.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 7.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 7.5 = 9.810708435 Simplifying x + 7.5 = 9.810708435 Reorder the terms: 7.5 + x = 9.810708435 Solving 7.5 + x = 9.810708435 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 = 9.810708435 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.810708435 + -7.5 x = 9.810708435 + -7.5 Combine like terms: 9.810708435 + -7.5 = 2.310708435 x = 2.310708435 Simplifying x = 2.310708435Subproblem 2
x + 7.5 = -9.810708435 Simplifying x + 7.5 = -9.810708435 Reorder the terms: 7.5 + x = -9.810708435 Solving 7.5 + x = -9.810708435 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 = -9.810708435 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.810708435 + -7.5 x = -9.810708435 + -7.5 Combine like terms: -9.810708435 + -7.5 = -17.310708435 x = -17.310708435 Simplifying x = -17.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.310708435, -17.310708435}
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