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Simplifying 0 = 4x3 + -18x2 + 7x Reorder the terms: 0 = 7x + -18x2 + 4x3 Solving 0 = 7x + -18x2 + 4x3 Solving for variable 'x'. Remove the zero: -7x + 18x2 + -4x3 = 7x + -18x2 + 4x3 + -7x + 18x2 + -4x3 Reorder the terms: -7x + 18x2 + -4x3 = 7x + -7x + -18x2 + 18x2 + 4x3 + -4x3 Combine like terms: 7x + -7x = 0 -7x + 18x2 + -4x3 = 0 + -18x2 + 18x2 + 4x3 + -4x3 -7x + 18x2 + -4x3 = -18x2 + 18x2 + 4x3 + -4x3 Combine like terms: -18x2 + 18x2 = 0 -7x + 18x2 + -4x3 = 0 + 4x3 + -4x3 -7x + 18x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -7x + 18x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 18x + -4x2) = 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 '(-7 + 18x + -4x2)' equal to zero and attempt to solve: Simplifying -7 + 18x + -4x2 = 0 Solving -7 + 18x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.75 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -4.5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -4.5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -4.5x + x2 = 0 + -1.75 -4.5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -4.5x + x2 = -1.75 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1.75 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1.75 + 5.0625 Combine like terms: -1.75 + 5.0625 = 3.3125 5.0625 + -4.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + -2.25) equal to 1.820027472 and -1.820027472.Subproblem 1
x + -2.25 = 1.820027472 Simplifying x + -2.25 = 1.820027472 Reorder the terms: -2.25 + x = 1.820027472 Solving -2.25 + x = 1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.820027472 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.820027472 + 2.25 x = 1.820027472 + 2.25 Combine like terms: 1.820027472 + 2.25 = 4.070027472 x = 4.070027472 Simplifying x = 4.070027472Subproblem 2
x + -2.25 = -1.820027472 Simplifying x + -2.25 = -1.820027472 Reorder the terms: -2.25 + x = -1.820027472 Solving -2.25 + x = -1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.820027472 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.820027472 + 2.25 x = -1.820027472 + 2.25 Combine like terms: -1.820027472 + 2.25 = 0.429972528 x = 0.429972528 Simplifying x = 0.429972528Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.070027472, 0.429972528}Solution
x = {0, 4.070027472, 0.429972528}
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