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Simplifying 2x + 3x2(4x + -5) = 0 Reorder the terms: 2x + 3x2(-5 + 4x) = 0 2x + (-5 * 3x2 + 4x * 3x2) = 0 2x + (-15x2 + 12x3) = 0 Solving 2x + -15x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -15x + 12x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2 + -15x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + -15x + 12x2 = 0 Solving 2 + -15x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.25x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.25x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + -0.1666666667 -1.25x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.25x + x2 = -0.1666666667 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.1666666667 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.1666666667 + 0.390625 Combine like terms: -0.1666666667 + 0.390625 = 0.2239583333 0.390625 + -1.25x + x2 = 0.2239583333 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.2239583333 Calculate the square root of the right side: 0.473242362 Break this problem into two subproblems by setting (x + -0.625) equal to 0.473242362 and -0.473242362.Subproblem 1
x + -0.625 = 0.473242362 Simplifying x + -0.625 = 0.473242362 Reorder the terms: -0.625 + x = 0.473242362 Solving -0.625 + x = 0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.473242362 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.473242362 + 0.625 x = 0.473242362 + 0.625 Combine like terms: 0.473242362 + 0.625 = 1.098242362 x = 1.098242362 Simplifying x = 1.098242362Subproblem 2
x + -0.625 = -0.473242362 Simplifying x + -0.625 = -0.473242362 Reorder the terms: -0.625 + x = -0.473242362 Solving -0.625 + x = -0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.473242362 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.473242362 + 0.625 x = -0.473242362 + 0.625 Combine like terms: -0.473242362 + 0.625 = 0.151757638 x = 0.151757638 Simplifying x = 0.151757638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.098242362, 0.151757638}Solution
x = {0, 1.098242362, 0.151757638}
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