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Simplifying (4x2 + 19x + -10) + -1(4x + -9) = 0 Reorder the terms: (-10 + 19x + 4x2) + -1(4x + -9) = 0 Remove parenthesis around (-10 + 19x + 4x2) -10 + 19x + 4x2 + -1(4x + -9) = 0 Reorder the terms: -10 + 19x + 4x2 + -1(-9 + 4x) = 0 -10 + 19x + 4x2 + (-9 * -1 + 4x * -1) = 0 -10 + 19x + 4x2 + (9 + -4x) = 0 Reorder the terms: -10 + 9 + 19x + -4x + 4x2 = 0 Combine like terms: -10 + 9 = -1 -1 + 19x + -4x + 4x2 = 0 Combine like terms: 19x + -4x = 15x -1 + 15x + 4x2 = 0 Solving -1 + 15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 3.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 3.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 3.75x + x2 = 0 + 0.25 3.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 3.75x + x2 = 0.25 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 0.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 0.25 + 3.515625 Combine like terms: 0.25 + 3.515625 = 3.765625 3.515625 + 3.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 1.875) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 1.875 = 1.940521837 Simplifying x + 1.875 = 1.940521837 Reorder the terms: 1.875 + x = 1.940521837 Solving 1.875 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 1.940521837 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.940521837 + -1.875 x = 1.940521837 + -1.875 Combine like terms: 1.940521837 + -1.875 = 0.065521837 x = 0.065521837 Simplifying x = 0.065521837Subproblem 2
x + 1.875 = -1.940521837 Simplifying x + 1.875 = -1.940521837 Reorder the terms: 1.875 + x = -1.940521837 Solving 1.875 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -1.940521837 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.940521837 + -1.875 x = -1.940521837 + -1.875 Combine like terms: -1.940521837 + -1.875 = -3.815521837 x = -3.815521837 Simplifying x = -3.815521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065521837, -3.815521837}
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