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Simplifying 4x2 + -36x + -15 = 0 Reorder the terms: -15 + -36x + 4x2 = 0 Solving -15 + -36x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -9x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -9x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -9x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -9x + x2 = 0 + 3.75 -9x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -9x + x2 = 3.75 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 3.75 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 3.75 + 20.25 Combine like terms: 3.75 + 20.25 = 24 20.25 + -9x + x2 = 24 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -4.5) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -4.5 = 4.898979486 Simplifying x + -4.5 = 4.898979486 Reorder the terms: -4.5 + x = 4.898979486 Solving -4.5 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.898979486 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.898979486 + 4.5 x = 4.898979486 + 4.5 Combine like terms: 4.898979486 + 4.5 = 9.398979486 x = 9.398979486 Simplifying x = 9.398979486Subproblem 2
x + -4.5 = -4.898979486 Simplifying x + -4.5 = -4.898979486 Reorder the terms: -4.5 + x = -4.898979486 Solving -4.5 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.898979486 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.898979486 + 4.5 x = -4.898979486 + 4.5 Combine like terms: -4.898979486 + 4.5 = -0.398979486 x = -0.398979486 Simplifying x = -0.398979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.398979486, -0.398979486}
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