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Simplifying 50 * 2 + -2x + -1x + -1x2 = 4x2 + 9 + 12x Multiply 50 * 2 100 + -2x + -1x + -1x2 = 4x2 + 9 + 12x Combine like terms: -2x + -1x = -3x 100 + -3x + -1x2 = 4x2 + 9 + 12x Reorder the terms: 100 + -3x + -1x2 = 9 + 12x + 4x2 Solving 100 + -3x + -1x2 = 9 + 12x + 4x2 Solving for variable 'x'. Reorder the terms: 100 + -9 + -3x + -12x + -1x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 100 + -9 = 91 91 + -3x + -12x + -1x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: -3x + -12x = -15x 91 + -15x + -1x2 + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 91 + -15x + -5x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Reorder the terms: 91 + -15x + -5x2 = 9 + -9 + 12x + -12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 91 + -15x + -5x2 = 0 + 12x + -12x + 4x2 + -4x2 91 + -15x + -5x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 91 + -15x + -5x2 = 0 + 4x2 + -4x2 91 + -15x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 91 + -15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -18.2 + 3x + x2 = 0 Move the constant term to the right: Add '18.2' to each side of the equation. -18.2 + 3x + 18.2 + x2 = 0 + 18.2 Reorder the terms: -18.2 + 18.2 + 3x + x2 = 0 + 18.2 Combine like terms: -18.2 + 18.2 = 0.0 0.0 + 3x + x2 = 0 + 18.2 3x + x2 = 0 + 18.2 Combine like terms: 0 + 18.2 = 18.2 3x + x2 = 18.2 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 18.2 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 18.2 + 2.25 Combine like terms: 18.2 + 2.25 = 20.45 2.25 + 3x + x2 = 20.45 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 20.45 Calculate the square root of the right side: 4.522167622 Break this problem into two subproblems by setting (x + 1.5) equal to 4.522167622 and -4.522167622.Subproblem 1
x + 1.5 = 4.522167622 Simplifying x + 1.5 = 4.522167622 Reorder the terms: 1.5 + x = 4.522167622 Solving 1.5 + x = 4.522167622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.522167622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.522167622 + -1.5 x = 4.522167622 + -1.5 Combine like terms: 4.522167622 + -1.5 = 3.022167622 x = 3.022167622 Simplifying x = 3.022167622Subproblem 2
x + 1.5 = -4.522167622 Simplifying x + 1.5 = -4.522167622 Reorder the terms: 1.5 + x = -4.522167622 Solving 1.5 + x = -4.522167622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.522167622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.522167622 + -1.5 x = -4.522167622 + -1.5 Combine like terms: -4.522167622 + -1.5 = -6.022167622 x = -6.022167622 Simplifying x = -6.022167622Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.022167622, -6.022167622}
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