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Simplifying 2x2 + -6x + 10x3 + x2 = 18x2 Reorder the terms: -6x + 2x2 + x2 + 10x3 = 18x2 Combine like terms: 2x2 + x2 = 3x2 -6x + 3x2 + 10x3 = 18x2 Solving -6x + 3x2 + 10x3 = 18x2 Solving for variable 'x'. Reorder the terms: -6x + 3x2 + -18x2 + 10x3 = 18x2 + -18x2 Combine like terms: 3x2 + -18x2 = -15x2 -6x + -15x2 + 10x3 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -6x + -15x2 + 10x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -15x + 10x2) = 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 '(-6 + -15x + 10x2)' equal to zero and attempt to solve: Simplifying -6 + -15x + 10x2 = 0 Solving -6 + -15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.5x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.5x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.5x + x2 = 0 + 0.6 -1.5x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.5x + x2 = 0.6 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.6 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.6 + 0.5625 Combine like terms: 0.6 + 0.5625 = 1.1625 0.5625 + -1.5x + x2 = 1.1625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.1625 Calculate the square root of the right side: 1.078192933 Break this problem into two subproblems by setting (x + -0.75) equal to 1.078192933 and -1.078192933.Subproblem 1
x + -0.75 = 1.078192933 Simplifying x + -0.75 = 1.078192933 Reorder the terms: -0.75 + x = 1.078192933 Solving -0.75 + x = 1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.078192933 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.078192933 + 0.75 x = 1.078192933 + 0.75 Combine like terms: 1.078192933 + 0.75 = 1.828192933 x = 1.828192933 Simplifying x = 1.828192933Subproblem 2
x + -0.75 = -1.078192933 Simplifying x + -0.75 = -1.078192933 Reorder the terms: -0.75 + x = -1.078192933 Solving -0.75 + x = -1.078192933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.078192933 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.078192933 + 0.75 x = -1.078192933 + 0.75 Combine like terms: -1.078192933 + 0.75 = -0.328192933 x = -0.328192933 Simplifying x = -0.328192933Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.828192933, -0.328192933}Solution
x = {0, 1.828192933, -0.328192933}
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