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Simplifying 10x2 + 24x + -59 = 0 Reorder the terms: -59 + 24x + 10x2 = 0 Solving -59 + 24x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.9 + 2.4x + x2 = 0 Move the constant term to the right: Add '5.9' to each side of the equation. -5.9 + 2.4x + 5.9 + x2 = 0 + 5.9 Reorder the terms: -5.9 + 5.9 + 2.4x + x2 = 0 + 5.9 Combine like terms: -5.9 + 5.9 = 0.0 0.0 + 2.4x + x2 = 0 + 5.9 2.4x + x2 = 0 + 5.9 Combine like terms: 0 + 5.9 = 5.9 2.4x + x2 = 5.9 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 5.9 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 5.9 + 1.44 Combine like terms: 5.9 + 1.44 = 7.34 1.44 + 2.4x + x2 = 7.34 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 7.34 Calculate the square root of the right side: 2.709243437 Break this problem into two subproblems by setting (x + 1.2) equal to 2.709243437 and -2.709243437.Subproblem 1
x + 1.2 = 2.709243437 Simplifying x + 1.2 = 2.709243437 Reorder the terms: 1.2 + x = 2.709243437 Solving 1.2 + x = 2.709243437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 2.709243437 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.709243437 + -1.2 x = 2.709243437 + -1.2 Combine like terms: 2.709243437 + -1.2 = 1.509243437 x = 1.509243437 Simplifying x = 1.509243437Subproblem 2
x + 1.2 = -2.709243437 Simplifying x + 1.2 = -2.709243437 Reorder the terms: 1.2 + x = -2.709243437 Solving 1.2 + x = -2.709243437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -2.709243437 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.709243437 + -1.2 x = -2.709243437 + -1.2 Combine like terms: -2.709243437 + -1.2 = -3.909243437 x = -3.909243437 Simplifying x = -3.909243437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.509243437, -3.909243437}
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