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Simplifying 15x(7x + -6) = 54 Reorder the terms: 15x(-6 + 7x) = 54 (-6 * 15x + 7x * 15x) = 54 (-90x + 105x2) = 54 Solving -90x + 105x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -90x + 105x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -90x + 105x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + -30x + 35x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-18 + -30x + 35x2)' equal to zero and attempt to solve: Simplifying -18 + -30x + 35x2 = 0 Solving -18 + -30x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.5142857143 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.5142857143' to each side of the equation. -0.5142857143 + -0.8571428571x + 0.5142857143 + x2 = 0 + 0.5142857143 Reorder the terms: -0.5142857143 + 0.5142857143 + -0.8571428571x + x2 = 0 + 0.5142857143 Combine like terms: -0.5142857143 + 0.5142857143 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.5142857143 -0.8571428571x + x2 = 0 + 0.5142857143 Combine like terms: 0 + 0.5142857143 = 0.5142857143 -0.8571428571x + x2 = 0.5142857143 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.5142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.5142857143 + 0.1836734694 Combine like terms: 0.5142857143 + 0.1836734694 = 0.6979591837 0.1836734694 + -0.8571428571x + x2 = 0.6979591837 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.6979591837 Calculate the square root of the right side: 0.835439515 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.835439515 and -0.835439515.Subproblem 1
x + -0.4285714286 = 0.835439515 Simplifying x + -0.4285714286 = 0.835439515 Reorder the terms: -0.4285714286 + x = 0.835439515 Solving -0.4285714286 + x = 0.835439515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.835439515 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.835439515 + 0.4285714286 x = 0.835439515 + 0.4285714286 Combine like terms: 0.835439515 + 0.4285714286 = 1.2640109436 x = 1.2640109436 Simplifying x = 1.2640109436Subproblem 2
x + -0.4285714286 = -0.835439515 Simplifying x + -0.4285714286 = -0.835439515 Reorder the terms: -0.4285714286 + x = -0.835439515 Solving -0.4285714286 + x = -0.835439515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.835439515 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.835439515 + 0.4285714286 x = -0.835439515 + 0.4285714286 Combine like terms: -0.835439515 + 0.4285714286 = -0.4068680864 x = -0.4068680864 Simplifying x = -0.4068680864Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2640109436, -0.4068680864}Solution
x = {1.2640109436, -0.4068680864}
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