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Simplifying 15x + -1x2 = 18.75 Solving 15x + -1x2 = 18.75 Solving for variable 'x'. Reorder the terms: -18.75 + 15x + -1x2 = 18.75 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 -18.75 + 15x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18.75 + -15x + x2 = 0.00 Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + -15x + -18.75 + x2 = 0.00 + -18.75 Reorder the terms: 18.75 + -18.75 + -15x + x2 = 0.00 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + -15x + x2 = 0.00 + -18.75 -15x + x2 = 0.00 + -18.75 Combine like terms: 0.00 + -18.75 = -18.75 -15x + x2 = -18.75 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 = -18.75 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -18.75 + 56.25 Combine like terms: -18.75 + 56.25 = 37.5 56.25 + -15x + x2 = 37.5 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 37.5 Calculate the square root of the right side: 6.123724357 Break this problem into two subproblems by setting (x + -7.5) equal to 6.123724357 and -6.123724357.Subproblem 1
x + -7.5 = 6.123724357 Simplifying x + -7.5 = 6.123724357 Reorder the terms: -7.5 + x = 6.123724357 Solving -7.5 + x = 6.123724357 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 = 6.123724357 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.123724357 + 7.5 x = 6.123724357 + 7.5 Combine like terms: 6.123724357 + 7.5 = 13.623724357 x = 13.623724357 Simplifying x = 13.623724357Subproblem 2
x + -7.5 = -6.123724357 Simplifying x + -7.5 = -6.123724357 Reorder the terms: -7.5 + x = -6.123724357 Solving -7.5 + x = -6.123724357 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 = -6.123724357 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.123724357 + 7.5 x = -6.123724357 + 7.5 Combine like terms: -6.123724357 + 7.5 = 1.376275643 x = 1.376275643 Simplifying x = 1.376275643Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.623724357, 1.376275643}
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