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Simplifying x = -4.9x2 + 34.3x + 1.5 Reorder the terms: x = 1.5 + 34.3x + -4.9x2 Solving x = 1.5 + 34.3x + -4.9x2 Solving for variable 'x'. Reorder the terms: -1.5 + x + -34.3x + 4.9x2 = 1.5 + 34.3x + -4.9x2 + -1.5 + -34.3x + 4.9x2 Combine like terms: x + -34.3x = -33.3x -1.5 + -33.3x + 4.9x2 = 1.5 + 34.3x + -4.9x2 + -1.5 + -34.3x + 4.9x2 Reorder the terms: -1.5 + -33.3x + 4.9x2 = 1.5 + -1.5 + 34.3x + -34.3x + -4.9x2 + 4.9x2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -33.3x + 4.9x2 = 0.0 + 34.3x + -34.3x + -4.9x2 + 4.9x2 -1.5 + -33.3x + 4.9x2 = 34.3x + -34.3x + -4.9x2 + 4.9x2 Combine like terms: 34.3x + -34.3x = 0.0 -1.5 + -33.3x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -1.5 + -33.3x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1.5 + -33.3x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.306122449 + -6.795918367x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -6.795918367x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -6.795918367x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -6.795918367x + x2 = 0 + 0.306122449 -6.795918367x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -6.795918367x + x2 = 0.306122449 The x term is -6.795918367x. Take half its coefficient (-3.397959184). Square it (11.54612662) and add it to both sides. Add '11.54612662' to each side of the equation. -6.795918367x + 11.54612662 + x2 = 0.306122449 + 11.54612662 Reorder the terms: 11.54612662 + -6.795918367x + x2 = 0.306122449 + 11.54612662 Combine like terms: 0.306122449 + 11.54612662 = 11.852249069 11.54612662 + -6.795918367x + x2 = 11.852249069 Factor a perfect square on the left side: (x + -3.397959184)(x + -3.397959184) = 11.852249069 Calculate the square root of the right side: 3.442709553 Break this problem into two subproblems by setting (x + -3.397959184) equal to 3.442709553 and -3.442709553.Subproblem 1
x + -3.397959184 = 3.442709553 Simplifying x + -3.397959184 = 3.442709553 Reorder the terms: -3.397959184 + x = 3.442709553 Solving -3.397959184 + x = 3.442709553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.397959184' to each side of the equation. -3.397959184 + 3.397959184 + x = 3.442709553 + 3.397959184 Combine like terms: -3.397959184 + 3.397959184 = 0.000000000 0.000000000 + x = 3.442709553 + 3.397959184 x = 3.442709553 + 3.397959184 Combine like terms: 3.442709553 + 3.397959184 = 6.840668737 x = 6.840668737 Simplifying x = 6.840668737Subproblem 2
x + -3.397959184 = -3.442709553 Simplifying x + -3.397959184 = -3.442709553 Reorder the terms: -3.397959184 + x = -3.442709553 Solving -3.397959184 + x = -3.442709553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.397959184' to each side of the equation. -3.397959184 + 3.397959184 + x = -3.442709553 + 3.397959184 Combine like terms: -3.397959184 + 3.397959184 = 0.000000000 0.000000000 + x = -3.442709553 + 3.397959184 x = -3.442709553 + 3.397959184 Combine like terms: -3.442709553 + 3.397959184 = -0.044750369 x = -0.044750369 Simplifying x = -0.044750369Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.840668737, -0.044750369}
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