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Simplifying -4.9x2 + x + 148 = -3x + 68.8 Reorder the terms: 148 + x + -4.9x2 = -3x + 68.8 Reorder the terms: 148 + x + -4.9x2 = 68.8 + -3x Solving 148 + x + -4.9x2 = 68.8 + -3x Solving for variable 'x'. Reorder the terms: 148 + -68.8 + x + 3x + -4.9x2 = 68.8 + -3x + -68.8 + 3x Combine like terms: 148 + -68.8 = 79.2 79.2 + x + 3x + -4.9x2 = 68.8 + -3x + -68.8 + 3x Combine like terms: x + 3x = 4x 79.2 + 4x + -4.9x2 = 68.8 + -3x + -68.8 + 3x Reorder the terms: 79.2 + 4x + -4.9x2 = 68.8 + -68.8 + -3x + 3x Combine like terms: 68.8 + -68.8 = 0.0 79.2 + 4x + -4.9x2 = 0.0 + -3x + 3x 79.2 + 4x + -4.9x2 = -3x + 3x Combine like terms: -3x + 3x = 0 79.2 + 4x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -16.16326531 + -0.8163265306x + x2 = 0 Move the constant term to the right: Add '16.16326531' to each side of the equation. -16.16326531 + -0.8163265306x + 16.16326531 + x2 = 0 + 16.16326531 Reorder the terms: -16.16326531 + 16.16326531 + -0.8163265306x + x2 = 0 + 16.16326531 Combine like terms: -16.16326531 + 16.16326531 = 0.00000000 0.00000000 + -0.8163265306x + x2 = 0 + 16.16326531 -0.8163265306x + x2 = 0 + 16.16326531 Combine like terms: 0 + 16.16326531 = 16.16326531 -0.8163265306x + x2 = 16.16326531 The x term is -0.8163265306x. Take half its coefficient (-0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. -0.8163265306x + 0.1665972511 + x2 = 16.16326531 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306x + x2 = 16.16326531 + 0.1665972511 Combine like terms: 16.16326531 + 0.1665972511 = 16.3298625611 0.1665972511 + -0.8163265306x + x2 = 16.3298625611 Factor a perfect square on the left side: (x + -0.4081632653)(x + -0.4081632653) = 16.3298625611 Calculate the square root of the right side: 4.041022465 Break this problem into two subproblems by setting (x + -0.4081632653) equal to 4.041022465 and -4.041022465.Subproblem 1
x + -0.4081632653 = 4.041022465 Simplifying x + -0.4081632653 = 4.041022465 Reorder the terms: -0.4081632653 + x = 4.041022465 Solving -0.4081632653 + x = 4.041022465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + x = 4.041022465 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = 4.041022465 + 0.4081632653 x = 4.041022465 + 0.4081632653 Combine like terms: 4.041022465 + 0.4081632653 = 4.4491857303 x = 4.4491857303 Simplifying x = 4.4491857303Subproblem 2
x + -0.4081632653 = -4.041022465 Simplifying x + -0.4081632653 = -4.041022465 Reorder the terms: -0.4081632653 + x = -4.041022465 Solving -0.4081632653 + x = -4.041022465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + x = -4.041022465 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + x = -4.041022465 + 0.4081632653 x = -4.041022465 + 0.4081632653 Combine like terms: -4.041022465 + 0.4081632653 = -3.6328591997 x = -3.6328591997 Simplifying x = -3.6328591997Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4491857303, -3.6328591997}
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