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Simplifying 15x3 + -70x2 + 63x = 0 Reorder the terms: 63x + -70x2 + 15x3 = 0 Solving 63x + -70x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(63 + -70x + 15x2) = 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 '(63 + -70x + 15x2)' equal to zero and attempt to solve: Simplifying 63 + -70x + 15x2 = 0 Solving 63 + -70x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 4.2 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -4.666666667x + -4.2 + x2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -4.666666667x + x2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -4.666666667x + x2 = 0 + -4.2 -4.666666667x + x2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -4.666666667x + x2 = -4.2 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -4.2 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -4.2 + 5.444444448 Combine like terms: -4.2 + 5.444444448 = 1.244444448 5.444444448 + -4.666666667x + x2 = 1.244444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 1.244444448 Calculate the square root of the right side: 1.115546704 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.115546704 and -1.115546704.Subproblem 1
x + -2.333333334 = 1.115546704 Simplifying x + -2.333333334 = 1.115546704 Reorder the terms: -2.333333334 + x = 1.115546704 Solving -2.333333334 + x = 1.115546704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 1.115546704 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.115546704 + 2.333333334 x = 1.115546704 + 2.333333334 Combine like terms: 1.115546704 + 2.333333334 = 3.448880038 x = 3.448880038 Simplifying x = 3.448880038Subproblem 2
x + -2.333333334 = -1.115546704 Simplifying x + -2.333333334 = -1.115546704 Reorder the terms: -2.333333334 + x = -1.115546704 Solving -2.333333334 + x = -1.115546704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -1.115546704 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.115546704 + 2.333333334 x = -1.115546704 + 2.333333334 Combine like terms: -1.115546704 + 2.333333334 = 1.21778663 x = 1.21778663 Simplifying x = 1.21778663Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.448880038, 1.21778663}Solution
x = {0, 3.448880038, 1.21778663}
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