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Simplifying 23 = 3x(x + 3) Reorder the terms: 23 = 3x(3 + x) 23 = (3 * 3x + x * 3x) 23 = (9x + 3x2) Solving 23 = 9x + 3x2 Solving for variable 'x'. Reorder the terms: 23 + -9x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 23 + -9x + -3x2 = 0 + 3x2 + -3x2 23 + -9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 23 + -9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 3x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 3x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 7.666666667 3x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 3x + x2 = 7.666666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 7.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7.666666667 + 2.25 Combine like terms: 7.666666667 + 2.25 = 9.916666667 2.25 + 3x + x2 = 9.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 9.916666667 Calculate the square root of the right side: 3.149073938 Break this problem into two subproblems by setting (x + 1.5) equal to 3.149073938 and -3.149073938.Subproblem 1
x + 1.5 = 3.149073938 Simplifying x + 1.5 = 3.149073938 Reorder the terms: 1.5 + x = 3.149073938 Solving 1.5 + x = 3.149073938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.149073938 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.149073938 + -1.5 x = 3.149073938 + -1.5 Combine like terms: 3.149073938 + -1.5 = 1.649073938 x = 1.649073938 Simplifying x = 1.649073938Subproblem 2
x + 1.5 = -3.149073938 Simplifying x + 1.5 = -3.149073938 Reorder the terms: 1.5 + x = -3.149073938 Solving 1.5 + x = -3.149073938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.149073938 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.149073938 + -1.5 x = -3.149073938 + -1.5 Combine like terms: -3.149073938 + -1.5 = -4.649073938 x = -4.649073938 Simplifying x = -4.649073938Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.649073938, -4.649073938}
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