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Simplifying 3x2 + 4x = 99 Reorder the terms: 4x + 3x2 = 99 Solving 4x + 3x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 4x + 3x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 1.333333333x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 1.333333333x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 1.333333333x + x2 = 0 + 33 1.333333333x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 1.333333333x + x2 = 33 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 33 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 33 + 0.4444444442 Combine like terms: 33 + 0.4444444442 = 33.4444444442 0.4444444442 + 1.333333333x + x2 = 33.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 33.4444444442 Calculate the square root of the right side: 5.783117191 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 5.783117191 and -5.783117191.Subproblem 1
x + 0.6666666665 = 5.783117191 Simplifying x + 0.6666666665 = 5.783117191 Reorder the terms: 0.6666666665 + x = 5.783117191 Solving 0.6666666665 + x = 5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 5.783117191 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 5.783117191 + -0.6666666665 x = 5.783117191 + -0.6666666665 Combine like terms: 5.783117191 + -0.6666666665 = 5.1164505245 x = 5.1164505245 Simplifying x = 5.1164505245Subproblem 2
x + 0.6666666665 = -5.783117191 Simplifying x + 0.6666666665 = -5.783117191 Reorder the terms: 0.6666666665 + x = -5.783117191 Solving 0.6666666665 + x = -5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -5.783117191 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -5.783117191 + -0.6666666665 x = -5.783117191 + -0.6666666665 Combine like terms: -5.783117191 + -0.6666666665 = -6.4497838575 x = -6.4497838575 Simplifying x = -6.4497838575Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1164505245, -6.4497838575}
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