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Simplifying 6(x2 + -15x + 21) = 0 Reorder the terms: 6(21 + -15x + x2) = 0 (21 * 6 + -15x * 6 + x2 * 6) = 0 (126 + -90x + 6x2) = 0 Solving 126 + -90x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(21 + -15x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(21 + -15x + x2)' equal to zero and attempt to solve: Simplifying 21 + -15x + x2 = 0 Solving 21 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -15x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -15x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -15x + x2 = 0 + -21 -15x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -15x + x2 = -21 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -21 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -21 + 56.25 Combine like terms: -21 + 56.25 = 35.25 56.25 + -15x + x2 = 35.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -7.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -7.5 = 5.937171044 Simplifying x + -7.5 = 5.937171044 Reorder the terms: -7.5 + x = 5.937171044 Solving -7.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.937171044 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.937171044 + 7.5 x = 5.937171044 + 7.5 Combine like terms: 5.937171044 + 7.5 = 13.437171044 x = 13.437171044 Simplifying x = 13.437171044Subproblem 2
x + -7.5 = -5.937171044 Simplifying x + -7.5 = -5.937171044 Reorder the terms: -7.5 + x = -5.937171044 Solving -7.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.937171044 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.937171044 + 7.5 x = -5.937171044 + 7.5 Combine like terms: -5.937171044 + 7.5 = 1.562828956 x = 1.562828956 Simplifying x = 1.562828956Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.437171044, 1.562828956}Solution
x = {13.437171044, 1.562828956}
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