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Simplifying -0.8x2 + 12x + 25.8 = 0 Reorder the terms: 25.8 + 12x + -0.8x2 = 0 Solving 25.8 + 12x + -0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -32.25 + -15x + x2 = 0 Move the constant term to the right: Add '32.25' to each side of the equation. -32.25 + -15x + 32.25 + x2 = 0 + 32.25 Reorder the terms: -32.25 + 32.25 + -15x + x2 = 0 + 32.25 Combine like terms: -32.25 + 32.25 = 0.00 0.00 + -15x + x2 = 0 + 32.25 -15x + x2 = 0 + 32.25 Combine like terms: 0 + 32.25 = 32.25 -15x + x2 = 32.25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 32.25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 32.25 + 56.25 Combine like terms: 32.25 + 56.25 = 88.5 56.25 + -15x + x2 = 88.5 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 88.5 Calculate the square root of the right side: 9.407443861 Break this problem into two subproblems by setting (x + -7.5) equal to 9.407443861 and -9.407443861.Subproblem 1
x + -7.5 = 9.407443861 Simplifying x + -7.5 = 9.407443861 Reorder the terms: -7.5 + x = 9.407443861 Solving -7.5 + x = 9.407443861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 9.407443861 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 9.407443861 + 7.5 x = 9.407443861 + 7.5 Combine like terms: 9.407443861 + 7.5 = 16.907443861 x = 16.907443861 Simplifying x = 16.907443861Subproblem 2
x + -7.5 = -9.407443861 Simplifying x + -7.5 = -9.407443861 Reorder the terms: -7.5 + x = -9.407443861 Solving -7.5 + x = -9.407443861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -9.407443861 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -9.407443861 + 7.5 x = -9.407443861 + 7.5 Combine like terms: -9.407443861 + 7.5 = -1.907443861 x = -1.907443861 Simplifying x = -1.907443861Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.907443861, -1.907443861}
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