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Simplifying 23x2 + -30x + 9 = 81 Reorder the terms: 9 + -30x + 23x2 = 81 Solving 9 + -30x + 23x2 = 81 Solving for variable 'x'. Reorder the terms: 9 + -81 + -30x + 23x2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + -30x + 23x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + -30x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -3.130434783 + -1.304347826x + x2 = 0 Move the constant term to the right: Add '3.130434783' to each side of the equation. -3.130434783 + -1.304347826x + 3.130434783 + x2 = 0 + 3.130434783 Reorder the terms: -3.130434783 + 3.130434783 + -1.304347826x + x2 = 0 + 3.130434783 Combine like terms: -3.130434783 + 3.130434783 = 0.000000000 0.000000000 + -1.304347826x + x2 = 0 + 3.130434783 -1.304347826x + x2 = 0 + 3.130434783 Combine like terms: 0 + 3.130434783 = 3.130434783 -1.304347826x + x2 = 3.130434783 The x term is -1.304347826x. Take half its coefficient (-0.652173913). Square it (0.4253308128) and add it to both sides. Add '0.4253308128' to each side of the equation. -1.304347826x + 0.4253308128 + x2 = 3.130434783 + 0.4253308128 Reorder the terms: 0.4253308128 + -1.304347826x + x2 = 3.130434783 + 0.4253308128 Combine like terms: 3.130434783 + 0.4253308128 = 3.5557655958 0.4253308128 + -1.304347826x + x2 = 3.5557655958 Factor a perfect square on the left side: (x + -0.652173913)(x + -0.652173913) = 3.5557655958 Calculate the square root of the right side: 1.885673778 Break this problem into two subproblems by setting (x + -0.652173913) equal to 1.885673778 and -1.885673778.Subproblem 1
x + -0.652173913 = 1.885673778 Simplifying x + -0.652173913 = 1.885673778 Reorder the terms: -0.652173913 + x = 1.885673778 Solving -0.652173913 + x = 1.885673778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.652173913' to each side of the equation. -0.652173913 + 0.652173913 + x = 1.885673778 + 0.652173913 Combine like terms: -0.652173913 + 0.652173913 = 0.000000000 0.000000000 + x = 1.885673778 + 0.652173913 x = 1.885673778 + 0.652173913 Combine like terms: 1.885673778 + 0.652173913 = 2.537847691 x = 2.537847691 Simplifying x = 2.537847691Subproblem 2
x + -0.652173913 = -1.885673778 Simplifying x + -0.652173913 = -1.885673778 Reorder the terms: -0.652173913 + x = -1.885673778 Solving -0.652173913 + x = -1.885673778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.652173913' to each side of the equation. -0.652173913 + 0.652173913 + x = -1.885673778 + 0.652173913 Combine like terms: -0.652173913 + 0.652173913 = 0.000000000 0.000000000 + x = -1.885673778 + 0.652173913 x = -1.885673778 + 0.652173913 Combine like terms: -1.885673778 + 0.652173913 = -1.233499865 x = -1.233499865 Simplifying x = -1.233499865Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.537847691, -1.233499865}
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