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Simplifying 2x2 + -3x = 62 Reorder the terms: -3x + 2x2 = 62 Solving -3x + 2x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + -3x + 2x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31 + -1.5x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -1.5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -1.5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1.5x + x2 = 0 + 31 -1.5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -1.5x + x2 = 31 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 = 31 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 31 + 0.5625 Combine like terms: 31 + 0.5625 = 31.5625 0.5625 + -1.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + -0.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + -0.75 = 5.618051264 Simplifying x + -0.75 = 5.618051264 Reorder the terms: -0.75 + x = 5.618051264 Solving -0.75 + x = 5.618051264 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 = 5.618051264 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.618051264 + 0.75 x = 5.618051264 + 0.75 Combine like terms: 5.618051264 + 0.75 = 6.368051264 x = 6.368051264 Simplifying x = 6.368051264Subproblem 2
x + -0.75 = -5.618051264 Simplifying x + -0.75 = -5.618051264 Reorder the terms: -0.75 + x = -5.618051264 Solving -0.75 + x = -5.618051264 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 = -5.618051264 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.618051264 + 0.75 x = -5.618051264 + 0.75 Combine like terms: -5.618051264 + 0.75 = -4.868051264 x = -4.868051264 Simplifying x = -4.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.368051264, -4.868051264}
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