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Simplifying -2x2 + 21x + 15 = 0 Reorder the terms: 15 + 21x + -2x2 = 0 Solving 15 + 21x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -10.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -10.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -10.5x + x2 = 0 + 7.5 -10.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -10.5x + x2 = 7.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 7.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 7.5 + 27.5625 Combine like terms: 7.5 + 27.5625 = 35.0625 27.5625 + -10.5x + x2 = 35.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x + -5.25) equal to 5.921359641 and -5.921359641.Subproblem 1
x + -5.25 = 5.921359641 Simplifying x + -5.25 = 5.921359641 Reorder the terms: -5.25 + x = 5.921359641 Solving -5.25 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 5.921359641 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 5.921359641 + 5.25 x = 5.921359641 + 5.25 Combine like terms: 5.921359641 + 5.25 = 11.171359641 x = 11.171359641 Simplifying x = 11.171359641Subproblem 2
x + -5.25 = -5.921359641 Simplifying x + -5.25 = -5.921359641 Reorder the terms: -5.25 + x = -5.921359641 Solving -5.25 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -5.921359641 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -5.921359641 + 5.25 x = -5.921359641 + 5.25 Combine like terms: -5.921359641 + 5.25 = -0.671359641 x = -0.671359641 Simplifying x = -0.671359641Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.171359641, -0.671359641}
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