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Simplifying 4x + 3x(5x + -8) = 33 Reorder the terms: 4x + 3x(-8 + 5x) = 33 4x + (-8 * 3x + 5x * 3x) = 33 4x + (-24x + 15x2) = 33 Combine like terms: 4x + -24x = -20x -20x + 15x2 = 33 Solving -20x + 15x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -20x + 15x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -20x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.2 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -1.333333333x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -1.333333333x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -1.333333333x + x2 = 0 + 2.2 -1.333333333x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -1.333333333x + x2 = 2.2 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 = 2.2 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 2.2 + 0.4444444442 Combine like terms: 2.2 + 0.4444444442 = 2.6444444442 0.4444444442 + -1.333333333x + x2 = 2.6444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 2.6444444442 Calculate the square root of the right side: 1.626174789 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.626174789 and -1.626174789.Subproblem 1
x + -0.6666666665 = 1.626174789 Simplifying x + -0.6666666665 = 1.626174789 Reorder the terms: -0.6666666665 + x = 1.626174789 Solving -0.6666666665 + x = 1.626174789 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 = 1.626174789 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.626174789 + 0.6666666665 x = 1.626174789 + 0.6666666665 Combine like terms: 1.626174789 + 0.6666666665 = 2.2928414555 x = 2.2928414555 Simplifying x = 2.2928414555Subproblem 2
x + -0.6666666665 = -1.626174789 Simplifying x + -0.6666666665 = -1.626174789 Reorder the terms: -0.6666666665 + x = -1.626174789 Solving -0.6666666665 + x = -1.626174789 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 = -1.626174789 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.626174789 + 0.6666666665 x = -1.626174789 + 0.6666666665 Combine like terms: -1.626174789 + 0.6666666665 = -0.9595081225 x = -0.9595081225 Simplifying x = -0.9595081225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2928414555, -0.9595081225}
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