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Simplifying -0.25x2 + 1.15x + 3.25 = 0 Reorder the terms: 3.25 + 1.15x + -0.25x2 = 0 Solving 3.25 + 1.15x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -13 + -4.6x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -4.6x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -4.6x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4.6x + x2 = 0 + 13 -4.6x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4.6x + x2 = 13 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 13 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 13 + 5.29 Combine like terms: 13 + 5.29 = 18.29 5.29 + -4.6x + x2 = 18.29 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 18.29 Calculate the square root of the right side: 4.276680956 Break this problem into two subproblems by setting (x + -2.3) equal to 4.276680956 and -4.276680956.Subproblem 1
x + -2.3 = 4.276680956 Simplifying x + -2.3 = 4.276680956 Reorder the terms: -2.3 + x = 4.276680956 Solving -2.3 + x = 4.276680956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 4.276680956 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 4.276680956 + 2.3 x = 4.276680956 + 2.3 Combine like terms: 4.276680956 + 2.3 = 6.576680956 x = 6.576680956 Simplifying x = 6.576680956Subproblem 2
x + -2.3 = -4.276680956 Simplifying x + -2.3 = -4.276680956 Reorder the terms: -2.3 + x = -4.276680956 Solving -2.3 + x = -4.276680956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -4.276680956 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -4.276680956 + 2.3 x = -4.276680956 + 2.3 Combine like terms: -4.276680956 + 2.3 = -1.976680956 x = -1.976680956 Simplifying x = -1.976680956Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.576680956, -1.976680956}
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