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Simplifying 3x4 + 20x3 + -18x2 = 0 Reorder the terms: -18x2 + 20x3 + 3x4 = 0 Solving -18x2 + 20x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-18 + 20x + 3x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-18 + 20x + 3x2)' equal to zero and attempt to solve: Simplifying -18 + 20x + 3x2 = 0 Solving -18 + 20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 6.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 6.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6.666666667x + x2 = 0 + 6 6.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 6.666666667x + x2 = 6 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 6 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 6 + 11.11111112 Combine like terms: 6 + 11.11111112 = 17.11111112 11.11111112 + 6.666666667x + x2 = 17.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 17.11111112 Calculate the square root of the right side: 4.136557883 Break this problem into two subproblems by setting (x + 3.333333334) equal to 4.136557883 and -4.136557883.Subproblem 1
x + 3.333333334 = 4.136557883 Simplifying x + 3.333333334 = 4.136557883 Reorder the terms: 3.333333334 + x = 4.136557883 Solving 3.333333334 + x = 4.136557883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 4.136557883 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 4.136557883 + -3.333333334 x = 4.136557883 + -3.333333334 Combine like terms: 4.136557883 + -3.333333334 = 0.803224549 x = 0.803224549 Simplifying x = 0.803224549Subproblem 2
x + 3.333333334 = -4.136557883 Simplifying x + 3.333333334 = -4.136557883 Reorder the terms: 3.333333334 + x = -4.136557883 Solving 3.333333334 + x = -4.136557883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -4.136557883 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -4.136557883 + -3.333333334 x = -4.136557883 + -3.333333334 Combine like terms: -4.136557883 + -3.333333334 = -7.469891217 x = -7.469891217 Simplifying x = -7.469891217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.803224549, -7.469891217}Solution
x = {0, 0.803224549, -7.469891217}
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