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Simplifying 15x2 = 9x + 56 Reorder the terms: 15x2 = 56 + 9x Solving 15x2 = 56 + 9x Solving for variable 'x'. Reorder the terms: -56 + -9x + 15x2 = 56 + 9x + -56 + -9x Reorder the terms: -56 + -9x + 15x2 = 56 + -56 + 9x + -9x Combine like terms: 56 + -56 = 0 -56 + -9x + 15x2 = 0 + 9x + -9x -56 + -9x + 15x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -56 + -9x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -3.733333333 + -0.6x + x2 = 0 Move the constant term to the right: Add '3.733333333' to each side of the equation. -3.733333333 + -0.6x + 3.733333333 + x2 = 0 + 3.733333333 Reorder the terms: -3.733333333 + 3.733333333 + -0.6x + x2 = 0 + 3.733333333 Combine like terms: -3.733333333 + 3.733333333 = 0.000000000 0.000000000 + -0.6x + x2 = 0 + 3.733333333 -0.6x + x2 = 0 + 3.733333333 Combine like terms: 0 + 3.733333333 = 3.733333333 -0.6x + x2 = 3.733333333 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 3.733333333 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 3.733333333 + 0.09 Combine like terms: 3.733333333 + 0.09 = 3.823333333 0.09 + -0.6x + x2 = 3.823333333 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 3.823333333 Calculate the square root of the right side: 1.955334583 Break this problem into two subproblems by setting (x + -0.3) equal to 1.955334583 and -1.955334583.Subproblem 1
x + -0.3 = 1.955334583 Simplifying x + -0.3 = 1.955334583 Reorder the terms: -0.3 + x = 1.955334583 Solving -0.3 + x = 1.955334583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.955334583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.955334583 + 0.3 x = 1.955334583 + 0.3 Combine like terms: 1.955334583 + 0.3 = 2.255334583 x = 2.255334583 Simplifying x = 2.255334583Subproblem 2
x + -0.3 = -1.955334583 Simplifying x + -0.3 = -1.955334583 Reorder the terms: -0.3 + x = -1.955334583 Solving -0.3 + x = -1.955334583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.955334583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.955334583 + 0.3 x = -1.955334583 + 0.3 Combine like terms: -1.955334583 + 0.3 = -1.655334583 x = -1.655334583 Simplifying x = -1.655334583Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.255334583, -1.655334583}
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