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Simplifying 4x2 + 15x + -3 + -1(-3x2 + 5) = 0 Reorder the terms: 4x2 + 15x + -3 + -1(5 + -3x2) = 0 4x2 + 15x + -3 + (5 * -1 + -3x2 * -1) = 0 4x2 + 15x + -3 + (-5 + 3x2) = 0 Reorder the terms: -3 + -5 + 15x + 4x2 + 3x2 = 0 Combine like terms: -3 + -5 = -8 -8 + 15x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -8 + 15x + 7x2 = 0 Solving -8 + 15x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 2.142857143x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 2.142857143x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 2.142857143x + x2 = 0 + 1.142857143 2.142857143x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 2.142857143x + x2 = 1.142857143 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = 1.142857143 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 1.142857143 + 1.147959185 Combine like terms: 1.142857143 + 1.147959185 = 2.290816328 1.147959185 + 2.142857143x + x2 = 2.290816328 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 2.290816328 Calculate the square root of the right side: 1.513544293 Break this problem into two subproblems by setting (x + 1.071428572) equal to 1.513544293 and -1.513544293.Subproblem 1
x + 1.071428572 = 1.513544293 Simplifying x + 1.071428572 = 1.513544293 Reorder the terms: 1.071428572 + x = 1.513544293 Solving 1.071428572 + x = 1.513544293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 1.513544293 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 1.513544293 + -1.071428572 x = 1.513544293 + -1.071428572 Combine like terms: 1.513544293 + -1.071428572 = 0.442115721 x = 0.442115721 Simplifying x = 0.442115721Subproblem 2
x + 1.071428572 = -1.513544293 Simplifying x + 1.071428572 = -1.513544293 Reorder the terms: 1.071428572 + x = -1.513544293 Solving 1.071428572 + x = -1.513544293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -1.513544293 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -1.513544293 + -1.071428572 x = -1.513544293 + -1.071428572 Combine like terms: -1.513544293 + -1.071428572 = -2.584972865 x = -2.584972865 Simplifying x = -2.584972865Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.442115721, -2.584972865}
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