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Simplifying 3x2 + 4x = 150 Reorder the terms: 4x + 3x2 = 150 Solving 4x + 3x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 4x + 3x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 1.333333333x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 1.333333333x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 1.333333333x + x2 = 0 + 50 1.333333333x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 1.333333333x + x2 = 50 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 = 50 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 50 + 0.4444444442 Combine like terms: 50 + 0.4444444442 = 50.4444444442 0.4444444442 + 1.333333333x + x2 = 50.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 50.4444444442 Calculate the square root of the right side: 7.102425251 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 7.102425251 and -7.102425251.Subproblem 1
x + 0.6666666665 = 7.102425251 Simplifying x + 0.6666666665 = 7.102425251 Reorder the terms: 0.6666666665 + x = 7.102425251 Solving 0.6666666665 + x = 7.102425251 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 = 7.102425251 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 7.102425251 + -0.6666666665 x = 7.102425251 + -0.6666666665 Combine like terms: 7.102425251 + -0.6666666665 = 6.4357585845 x = 6.4357585845 Simplifying x = 6.4357585845Subproblem 2
x + 0.6666666665 = -7.102425251 Simplifying x + 0.6666666665 = -7.102425251 Reorder the terms: 0.6666666665 + x = -7.102425251 Solving 0.6666666665 + x = -7.102425251 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 = -7.102425251 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -7.102425251 + -0.6666666665 x = -7.102425251 + -0.6666666665 Combine like terms: -7.102425251 + -0.6666666665 = -7.7690919175 x = -7.7690919175 Simplifying x = -7.7690919175Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.4357585845, -7.7690919175}
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