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Simplifying -5x2 + 12x + 0.5 = 0 Reorder the terms: 0.5 + 12x + -5x2 = 0 Solving 0.5 + 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'. -0.1 + -2.4x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -2.4x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -2.4x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -2.4x + x2 = 0 + 0.1 -2.4x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -2.4x + x2 = 0.1 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 = 0.1 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 0.1 + 1.44 Combine like terms: 0.1 + 1.44 = 1.54 1.44 + -2.4x + x2 = 1.54 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.54 Calculate the square root of the right side: 1.240967365 Break this problem into two subproblems by setting (x + -1.2) equal to 1.240967365 and -1.240967365.Subproblem 1
x + -1.2 = 1.240967365 Simplifying x + -1.2 = 1.240967365 Reorder the terms: -1.2 + x = 1.240967365 Solving -1.2 + x = 1.240967365 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 = 1.240967365 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.240967365 + 1.2 x = 1.240967365 + 1.2 Combine like terms: 1.240967365 + 1.2 = 2.440967365 x = 2.440967365 Simplifying x = 2.440967365Subproblem 2
x + -1.2 = -1.240967365 Simplifying x + -1.2 = -1.240967365 Reorder the terms: -1.2 + x = -1.240967365 Solving -1.2 + x = -1.240967365 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 = -1.240967365 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.240967365 + 1.2 x = -1.240967365 + 1.2 Combine like terms: -1.240967365 + 1.2 = -0.040967365 x = -0.040967365 Simplifying x = -0.040967365Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.440967365, -0.040967365}
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