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Simplifying 0 = 4x2 + -7x + -3 Reorder the terms: 0 = -3 + -7x + 4x2 Solving 0 = -3 + -7x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + 7x + -4x2 = -3 + -7x + 4x2 + 3 + 7x + -4x2 Reorder the terms: 3 + 7x + -4x2 = -3 + 3 + -7x + 7x + 4x2 + -4x2 Combine like terms: -3 + 3 = 0 3 + 7x + -4x2 = 0 + -7x + 7x + 4x2 + -4x2 3 + 7x + -4x2 = -7x + 7x + 4x2 + -4x2 Combine like terms: -7x + 7x = 0 3 + 7x + -4x2 = 0 + 4x2 + -4x2 3 + 7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.75x + x2 = 0 + 0.75 -1.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.75x + x2 = 0.75 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 = 0.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 0.75 + 0.765625 Combine like terms: 0.75 + 0.765625 = 1.515625 0.765625 + -1.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -0.875) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -0.875 = 1.231107225 Simplifying x + -0.875 = 1.231107225 Reorder the terms: -0.875 + x = 1.231107225 Solving -0.875 + x = 1.231107225 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 = 1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.231107225 + 0.875 x = 1.231107225 + 0.875 Combine like terms: 1.231107225 + 0.875 = 2.106107225 x = 2.106107225 Simplifying x = 2.106107225Subproblem 2
x + -0.875 = -1.231107225 Simplifying x + -0.875 = -1.231107225 Reorder the terms: -0.875 + x = -1.231107225 Solving -0.875 + x = -1.231107225 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 = -1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.231107225 + 0.875 x = -1.231107225 + 0.875 Combine like terms: -1.231107225 + 0.875 = -0.356107225 x = -0.356107225 Simplifying x = -0.356107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.106107225, -0.356107225}
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