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Simplifying 5x(3x + -6) = 22 Reorder the terms: 5x(-6 + 3x) = 22 (-6 * 5x + 3x * 5x) = 22 (-30x + 15x2) = 22 Solving -30x + 15x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + -30x + 15x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + -30x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.466666667 + -2x + x2 = 0 Move the constant term to the right: Add '1.466666667' to each side of the equation. -1.466666667 + -2x + 1.466666667 + x2 = 0 + 1.466666667 Reorder the terms: -1.466666667 + 1.466666667 + -2x + x2 = 0 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.466666667 -2x + x2 = 0 + 1.466666667 Combine like terms: 0 + 1.466666667 = 1.466666667 -2x + x2 = 1.466666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.466666667 + 1 Reorder the terms: 1 + -2x + x2 = 1.466666667 + 1 Combine like terms: 1.466666667 + 1 = 2.466666667 1 + -2x + x2 = 2.466666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.466666667 Calculate the square root of the right side: 1.570562532 Break this problem into two subproblems by setting (x + -1) equal to 1.570562532 and -1.570562532.Subproblem 1
x + -1 = 1.570562532 Simplifying x + -1 = 1.570562532 Reorder the terms: -1 + x = 1.570562532 Solving -1 + x = 1.570562532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.570562532 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.570562532 + 1 x = 1.570562532 + 1 Combine like terms: 1.570562532 + 1 = 2.570562532 x = 2.570562532 Simplifying x = 2.570562532Subproblem 2
x + -1 = -1.570562532 Simplifying x + -1 = -1.570562532 Reorder the terms: -1 + x = -1.570562532 Solving -1 + x = -1.570562532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.570562532 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.570562532 + 1 x = -1.570562532 + 1 Combine like terms: -1.570562532 + 1 = -0.570562532 x = -0.570562532 Simplifying x = -0.570562532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.570562532, -0.570562532}
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