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Simplifying 130 = 2x2 + 3x Reorder the terms: 130 = 3x + 2x2 Solving 130 = 3x + 2x2 Solving for variable 'x'. Reorder the terms: 130 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 130 + -3x + -2x2 = 0 + 2x2 + -2x2 130 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 130 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -65 + 1.5x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + 1.5x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 1.5x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 1.5x + x2 = 0 + 65 1.5x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 1.5x + x2 = 65 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 65 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 65 + 0.5625 Combine like terms: 65 + 0.5625 = 65.5625 0.5625 + 1.5x + x2 = 65.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 65.5625 Calculate the square root of the right side: 8.09706737 Break this problem into two subproblems by setting (x + 0.75) equal to 8.09706737 and -8.09706737.Subproblem 1
x + 0.75 = 8.09706737 Simplifying x + 0.75 = 8.09706737 Reorder the terms: 0.75 + x = 8.09706737 Solving 0.75 + x = 8.09706737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 8.09706737 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.09706737 + -0.75 x = 8.09706737 + -0.75 Combine like terms: 8.09706737 + -0.75 = 7.34706737 x = 7.34706737 Simplifying x = 7.34706737Subproblem 2
x + 0.75 = -8.09706737 Simplifying x + 0.75 = -8.09706737 Reorder the terms: 0.75 + x = -8.09706737 Solving 0.75 + x = -8.09706737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -8.09706737 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.09706737 + -0.75 x = -8.09706737 + -0.75 Combine like terms: -8.09706737 + -0.75 = -8.84706737 x = -8.84706737 Simplifying x = -8.84706737Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.34706737, -8.84706737}
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