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Simplifying 0.33x2 + 4x + -15 = 0 Reorder the terms: -15 + 4x + 0.33x2 = 0 Solving -15 + 4x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -45.45454545 + 12.12121212x + x2 = 0 Move the constant term to the right: Add '45.45454545' to each side of the equation. -45.45454545 + 12.12121212x + 45.45454545 + x2 = 0 + 45.45454545 Reorder the terms: -45.45454545 + 45.45454545 + 12.12121212x + x2 = 0 + 45.45454545 Combine like terms: -45.45454545 + 45.45454545 = 0.00000000 0.00000000 + 12.12121212x + x2 = 0 + 45.45454545 12.12121212x + x2 = 0 + 45.45454545 Combine like terms: 0 + 45.45454545 = 45.45454545 12.12121212x + x2 = 45.45454545 The x term is 12.12121212x. Take half its coefficient (6.06060606). Square it (36.73094581) and add it to both sides. Add '36.73094581' to each side of the equation. 12.12121212x + 36.73094581 + x2 = 45.45454545 + 36.73094581 Reorder the terms: 36.73094581 + 12.12121212x + x2 = 45.45454545 + 36.73094581 Combine like terms: 45.45454545 + 36.73094581 = 82.18549126 36.73094581 + 12.12121212x + x2 = 82.18549126 Factor a perfect square on the left side: (x + 6.06060606)(x + 6.06060606) = 82.18549126 Calculate the square root of the right side: 9.065621394 Break this problem into two subproblems by setting (x + 6.06060606) equal to 9.065621394 and -9.065621394.Subproblem 1
x + 6.06060606 = 9.065621394 Simplifying x + 6.06060606 = 9.065621394 Reorder the terms: 6.06060606 + x = 9.065621394 Solving 6.06060606 + x = 9.065621394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.06060606' to each side of the equation. 6.06060606 + -6.06060606 + x = 9.065621394 + -6.06060606 Combine like terms: 6.06060606 + -6.06060606 = 0.00000000 0.00000000 + x = 9.065621394 + -6.06060606 x = 9.065621394 + -6.06060606 Combine like terms: 9.065621394 + -6.06060606 = 3.005015334 x = 3.005015334 Simplifying x = 3.005015334Subproblem 2
x + 6.06060606 = -9.065621394 Simplifying x + 6.06060606 = -9.065621394 Reorder the terms: 6.06060606 + x = -9.065621394 Solving 6.06060606 + x = -9.065621394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.06060606' to each side of the equation. 6.06060606 + -6.06060606 + x = -9.065621394 + -6.06060606 Combine like terms: 6.06060606 + -6.06060606 = 0.00000000 0.00000000 + x = -9.065621394 + -6.06060606 x = -9.065621394 + -6.06060606 Combine like terms: -9.065621394 + -6.06060606 = -15.126227454 x = -15.126227454 Simplifying x = -15.126227454Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.005015334, -15.126227454}
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