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Simplifying 4x2 + -30x + 45 = 11 Reorder the terms: 45 + -30x + 4x2 = 11 Solving 45 + -30x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: 45 + -11 + -30x + 4x2 = 11 + -11 Combine like terms: 45 + -11 = 34 34 + -30x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 34 + -30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -15x + 2x2)' equal to zero and attempt to solve: Simplifying 17 + -15x + 2x2 = 0 Solving 17 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -7.5x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -7.5x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -7.5x + x2 = 0 + -8.5 -7.5x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -7.5x + x2 = -8.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -8.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -8.5 + 14.0625 Combine like terms: -8.5 + 14.0625 = 5.5625 14.0625 + -7.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -3.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -3.75 = 2.358495283 Simplifying x + -3.75 = 2.358495283 Reorder the terms: -3.75 + x = 2.358495283 Solving -3.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 2.358495283 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.358495283 + 3.75 x = 2.358495283 + 3.75 Combine like terms: 2.358495283 + 3.75 = 6.108495283 x = 6.108495283 Simplifying x = 6.108495283Subproblem 2
x + -3.75 = -2.358495283 Simplifying x + -3.75 = -2.358495283 Reorder the terms: -3.75 + x = -2.358495283 Solving -3.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -2.358495283 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.358495283 + 3.75 x = -2.358495283 + 3.75 Combine like terms: -2.358495283 + 3.75 = 1.391504717 x = 1.391504717 Simplifying x = 1.391504717Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.108495283, 1.391504717}Solution
x = {6.108495283, 1.391504717}
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