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Simplifying 4x2 + -19 + 7 = -7x + 2 Reorder the terms: -19 + 7 + 4x2 = -7x + 2 Combine like terms: -19 + 7 = -12 -12 + 4x2 = -7x + 2 Reorder the terms: -12 + 4x2 = 2 + -7x Solving -12 + 4x2 = 2 + -7x Solving for variable 'x'. Reorder the terms: -12 + -2 + 7x + 4x2 = 2 + -7x + -2 + 7x Combine like terms: -12 + -2 = -14 -14 + 7x + 4x2 = 2 + -7x + -2 + 7x Reorder the terms: -14 + 7x + 4x2 = 2 + -2 + -7x + 7x Combine like terms: 2 + -2 = 0 -14 + 7x + 4x2 = 0 + -7x + 7x -14 + 7x + 4x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -14 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 1.75x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 1.75x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 1.75x + x2 = 0 + 3.5 1.75x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 1.75x + x2 = 3.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 3.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 3.5 + 0.765625 Combine like terms: 3.5 + 0.765625 = 4.265625 0.765625 + 1.75x + x2 = 4.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (x + 0.875) equal to 2.065338955 and -2.065338955.Subproblem 1
x + 0.875 = 2.065338955 Simplifying x + 0.875 = 2.065338955 Reorder the terms: 0.875 + x = 2.065338955 Solving 0.875 + x = 2.065338955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.065338955 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.065338955 + -0.875 x = 2.065338955 + -0.875 Combine like terms: 2.065338955 + -0.875 = 1.190338955 x = 1.190338955 Simplifying x = 1.190338955Subproblem 2
x + 0.875 = -2.065338955 Simplifying x + 0.875 = -2.065338955 Reorder the terms: 0.875 + x = -2.065338955 Solving 0.875 + x = -2.065338955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.065338955 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.065338955 + -0.875 x = -2.065338955 + -0.875 Combine like terms: -2.065338955 + -0.875 = -2.940338955 x = -2.940338955 Simplifying x = -2.940338955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.190338955, -2.940338955}
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