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Simplifying 2x2 + -3x + -24 = 0 Reorder the terms: -24 + -3x + 2x2 = 0 Solving -24 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -1.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -1.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.5x + x2 = 0 + 12 -1.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.5x + x2 = 12 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 = 12 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 12 + 0.5625 Combine like terms: 12 + 0.5625 = 12.5625 0.5625 + -1.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -0.75) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -0.75 = 3.54436172 Simplifying x + -0.75 = 3.54436172 Reorder the terms: -0.75 + x = 3.54436172 Solving -0.75 + x = 3.54436172 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 = 3.54436172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.54436172 + 0.75 x = 3.54436172 + 0.75 Combine like terms: 3.54436172 + 0.75 = 4.29436172 x = 4.29436172 Simplifying x = 4.29436172Subproblem 2
x + -0.75 = -3.54436172 Simplifying x + -0.75 = -3.54436172 Reorder the terms: -0.75 + x = -3.54436172 Solving -0.75 + x = -3.54436172 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 = -3.54436172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.54436172 + 0.75 x = -3.54436172 + 0.75 Combine like terms: -3.54436172 + 0.75 = -2.79436172 x = -2.79436172 Simplifying x = -2.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.29436172, -2.79436172}
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