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Simplifying 400 = 1.5x2 + -3x + 2.5 Reorder the terms: 400 = 2.5 + -3x + 1.5x2 Solving 400 = 2.5 + -3x + 1.5x2 Solving for variable 'x'. Combine like terms: 400 + -2.5 = 397.5 397.5 + 3x + -1.5x2 = 2.5 + -3x + 1.5x2 + -2.5 + 3x + -1.5x2 Reorder the terms: 397.5 + 3x + -1.5x2 = 2.5 + -2.5 + -3x + 3x + 1.5x2 + -1.5x2 Combine like terms: 2.5 + -2.5 = 0.0 397.5 + 3x + -1.5x2 = 0.0 + -3x + 3x + 1.5x2 + -1.5x2 397.5 + 3x + -1.5x2 = -3x + 3x + 1.5x2 + -1.5x2 Combine like terms: -3x + 3x = 0 397.5 + 3x + -1.5x2 = 0 + 1.5x2 + -1.5x2 397.5 + 3x + -1.5x2 = 1.5x2 + -1.5x2 Combine like terms: 1.5x2 + -1.5x2 = 0.0 397.5 + 3x + -1.5x2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -265 + -2x + x2 = 0 Move the constant term to the right: Add '265' to each side of the equation. -265 + -2x + 265 + x2 = 0 + 265 Reorder the terms: -265 + 265 + -2x + x2 = 0 + 265 Combine like terms: -265 + 265 = 0 0 + -2x + x2 = 0 + 265 -2x + x2 = 0 + 265 Combine like terms: 0 + 265 = 265 -2x + x2 = 265 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 265 + 1 Reorder the terms: 1 + -2x + x2 = 265 + 1 Combine like terms: 265 + 1 = 266 1 + -2x + x2 = 266 Factor a perfect square on the left side: (x + -1)(x + -1) = 266 Calculate the square root of the right side: 16.30950643 Break this problem into two subproblems by setting (x + -1) equal to 16.30950643 and -16.30950643.Subproblem 1
x + -1 = 16.30950643 Simplifying x + -1 = 16.30950643 Reorder the terms: -1 + x = 16.30950643 Solving -1 + x = 16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 16.30950643 + 1 Combine like terms: -1 + 1 = 0 0 + x = 16.30950643 + 1 x = 16.30950643 + 1 Combine like terms: 16.30950643 + 1 = 17.30950643 x = 17.30950643 Simplifying x = 17.30950643Subproblem 2
x + -1 = -16.30950643 Simplifying x + -1 = -16.30950643 Reorder the terms: -1 + x = -16.30950643 Solving -1 + x = -16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -16.30950643 + 1 Combine like terms: -1 + 1 = 0 0 + x = -16.30950643 + 1 x = -16.30950643 + 1 Combine like terms: -16.30950643 + 1 = -15.30950643 x = -15.30950643 Simplifying x = -15.30950643Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.30950643, -15.30950643}
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