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Simplifying (2x2 + 4x + 1) + (3x2 + -12x + -16) = 100 Reorder the terms: (1 + 4x + 2x2) + (3x2 + -12x + -16) = 100 Remove parenthesis around (1 + 4x + 2x2) 1 + 4x + 2x2 + (3x2 + -12x + -16) = 100 Reorder the terms: 1 + 4x + 2x2 + (-16 + -12x + 3x2) = 100 Remove parenthesis around (-16 + -12x + 3x2) 1 + 4x + 2x2 + -16 + -12x + 3x2 = 100 Reorder the terms: 1 + -16 + 4x + -12x + 2x2 + 3x2 = 100 Combine like terms: 1 + -16 = -15 -15 + 4x + -12x + 2x2 + 3x2 = 100 Combine like terms: 4x + -12x = -8x -15 + -8x + 2x2 + 3x2 = 100 Combine like terms: 2x2 + 3x2 = 5x2 -15 + -8x + 5x2 = 100 Solving -15 + -8x + 5x2 = 100 Solving for variable 'x'. Reorder the terms: -15 + -100 + -8x + 5x2 = 100 + -100 Combine like terms: -15 + -100 = -115 -115 + -8x + 5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -115 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -23 + -1.6x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -1.6x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -1.6x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1.6x + x2 = 0 + 23 -1.6x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -1.6x + x2 = 23 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 23 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 23 + 0.64 Combine like terms: 23 + 0.64 = 23.64 0.64 + -1.6x + x2 = 23.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 23.64 Calculate the square root of the right side: 4.862098312 Break this problem into two subproblems by setting (x + -0.8) equal to 4.862098312 and -4.862098312.Subproblem 1
x + -0.8 = 4.862098312 Simplifying x + -0.8 = 4.862098312 Reorder the terms: -0.8 + x = 4.862098312 Solving -0.8 + x = 4.862098312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 4.862098312 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 4.862098312 + 0.8 x = 4.862098312 + 0.8 Combine like terms: 4.862098312 + 0.8 = 5.662098312 x = 5.662098312 Simplifying x = 5.662098312Subproblem 2
x + -0.8 = -4.862098312 Simplifying x + -0.8 = -4.862098312 Reorder the terms: -0.8 + x = -4.862098312 Solving -0.8 + x = -4.862098312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -4.862098312 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -4.862098312 + 0.8 x = -4.862098312 + 0.8 Combine like terms: -4.862098312 + 0.8 = -4.062098312 x = -4.062098312 Simplifying x = -4.062098312Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.662098312, -4.062098312}
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