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Simplifying 3x2 + -63x + 42 = 0 Reorder the terms: 42 + -63x + 3x2 = 0 Solving 42 + -63x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -21x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -21x + x2)' equal to zero and attempt to solve: Simplifying 14 + -21x + x2 = 0 Solving 14 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -21x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -21x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -21x + x2 = 0 + -14 -21x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -21x + x2 = -14 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -14 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -14 + 110.25 Combine like terms: -14 + 110.25 = 96.25 110.25 + -21x + x2 = 96.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + -10.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + -10.5 = 9.810708435 Simplifying x + -10.5 = 9.810708435 Reorder the terms: -10.5 + x = 9.810708435 Solving -10.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.810708435 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.810708435 + 10.5 x = 9.810708435 + 10.5 Combine like terms: 9.810708435 + 10.5 = 20.310708435 x = 20.310708435 Simplifying x = 20.310708435Subproblem 2
x + -10.5 = -9.810708435 Simplifying x + -10.5 = -9.810708435 Reorder the terms: -10.5 + x = -9.810708435 Solving -10.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.810708435 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.810708435 + 10.5 x = -9.810708435 + 10.5 Combine like terms: -9.810708435 + 10.5 = 0.689291565 x = 0.689291565 Simplifying x = 0.689291565Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.310708435, 0.689291565}Solution
x = {20.310708435, 0.689291565}
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