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Simplifying 5x2 + -12x + -19 = 0 Reorder the terms: -19 + -12x + 5x2 = 0 Solving -19 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + -2.4x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + -2.4x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + -2.4x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -2.4x + x2 = 0 + 3.8 -2.4x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 -2.4x + x2 = 3.8 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 = 3.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 3.8 + 1.44 Combine like terms: 3.8 + 1.44 = 5.24 1.44 + -2.4x + x2 = 5.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 5.24 Calculate the square root of the right side: 2.289104628 Break this problem into two subproblems by setting (x + -1.2) equal to 2.289104628 and -2.289104628.Subproblem 1
x + -1.2 = 2.289104628 Simplifying x + -1.2 = 2.289104628 Reorder the terms: -1.2 + x = 2.289104628 Solving -1.2 + x = 2.289104628 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 = 2.289104628 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.289104628 + 1.2 x = 2.289104628 + 1.2 Combine like terms: 2.289104628 + 1.2 = 3.489104628 x = 3.489104628 Simplifying x = 3.489104628Subproblem 2
x + -1.2 = -2.289104628 Simplifying x + -1.2 = -2.289104628 Reorder the terms: -1.2 + x = -2.289104628 Solving -1.2 + x = -2.289104628 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 = -2.289104628 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.289104628 + 1.2 x = -2.289104628 + 1.2 Combine like terms: -2.289104628 + 1.2 = -1.089104628 x = -1.089104628 Simplifying x = -1.089104628Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.489104628, -1.089104628}
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