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Simplifying 30x2 + -87x + 46 = 0 Reorder the terms: 46 + -87x + 30x2 = 0 Solving 46 + -87x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 1.533333333 + -2.9x + x2 = 0 Move the constant term to the right: Add '-1.533333333' to each side of the equation. 1.533333333 + -2.9x + -1.533333333 + x2 = 0 + -1.533333333 Reorder the terms: 1.533333333 + -1.533333333 + -2.9x + x2 = 0 + -1.533333333 Combine like terms: 1.533333333 + -1.533333333 = 0.000000000 0.000000000 + -2.9x + x2 = 0 + -1.533333333 -2.9x + x2 = 0 + -1.533333333 Combine like terms: 0 + -1.533333333 = -1.533333333 -2.9x + x2 = -1.533333333 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = -1.533333333 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = -1.533333333 + 2.1025 Combine like terms: -1.533333333 + 2.1025 = 0.569166667 2.1025 + -2.9x + x2 = 0.569166667 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 0.569166667 Calculate the square root of the right side: 0.754431353 Break this problem into two subproblems by setting (x + -1.45) equal to 0.754431353 and -0.754431353.Subproblem 1
x + -1.45 = 0.754431353 Simplifying x + -1.45 = 0.754431353 Reorder the terms: -1.45 + x = 0.754431353 Solving -1.45 + x = 0.754431353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 0.754431353 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 0.754431353 + 1.45 x = 0.754431353 + 1.45 Combine like terms: 0.754431353 + 1.45 = 2.204431353 x = 2.204431353 Simplifying x = 2.204431353Subproblem 2
x + -1.45 = -0.754431353 Simplifying x + -1.45 = -0.754431353 Reorder the terms: -1.45 + x = -0.754431353 Solving -1.45 + x = -0.754431353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -0.754431353 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -0.754431353 + 1.45 x = -0.754431353 + 1.45 Combine like terms: -0.754431353 + 1.45 = 0.695568647 x = 0.695568647 Simplifying x = 0.695568647Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.204431353, 0.695568647}
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