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Simplifying 4x2 + 10x3 = 6x2 + 15x Reorder the terms: 4x2 + 10x3 = 15x + 6x2 Solving 4x2 + 10x3 = 15x + 6x2 Solving for variable 'x'. Reorder the terms: -15x + 4x2 + -6x2 + 10x3 = 15x + 6x2 + -15x + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 -15x + -2x2 + 10x3 = 15x + 6x2 + -15x + -6x2 Reorder the terms: -15x + -2x2 + 10x3 = 15x + -15x + 6x2 + -6x2 Combine like terms: 15x + -15x = 0 -15x + -2x2 + 10x3 = 0 + 6x2 + -6x2 -15x + -2x2 + 10x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15x + -2x2 + 10x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + -2x + 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 '(-15 + -2x + 10x2)' equal to zero and attempt to solve: Simplifying -15 + -2x + 10x2 = 0 Solving -15 + -2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -0.2x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.2x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.2x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.2x + x2 = 0 + 1.5 -0.2x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.2x + x2 = 1.5 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 1.5 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 1.5 + 0.01 Combine like terms: 1.5 + 0.01 = 1.51 0.01 + -0.2x + x2 = 1.51 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 1.51 Calculate the square root of the right side: 1.228820573 Break this problem into two subproblems by setting (x + -0.1) equal to 1.228820573 and -1.228820573.Subproblem 1
x + -0.1 = 1.228820573 Simplifying x + -0.1 = 1.228820573 Reorder the terms: -0.1 + x = 1.228820573 Solving -0.1 + x = 1.228820573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.228820573 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.228820573 + 0.1 x = 1.228820573 + 0.1 Combine like terms: 1.228820573 + 0.1 = 1.328820573 x = 1.328820573 Simplifying x = 1.328820573Subproblem 2
x + -0.1 = -1.228820573 Simplifying x + -0.1 = -1.228820573 Reorder the terms: -0.1 + x = -1.228820573 Solving -0.1 + x = -1.228820573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.228820573 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.228820573 + 0.1 x = -1.228820573 + 0.1 Combine like terms: -1.228820573 + 0.1 = -1.128820573 x = -1.128820573 Simplifying x = -1.128820573Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.328820573, -1.128820573}Solution
x = {0, 1.328820573, -1.128820573}
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