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Simplifying 4x2 + -3x + -84 = 0 Reorder the terms: -84 + -3x + 4x2 = 0 Solving -84 + -3x + 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'. -21 + -0.75x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -0.75x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -0.75x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -0.75x + x2 = 0 + 21 -0.75x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -0.75x + x2 = 21 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 21 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 21 + 0.140625 Combine like terms: 21 + 0.140625 = 21.140625 0.140625 + -0.75x + x2 = 21.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 21.140625 Calculate the square root of the right side: 4.597893539 Break this problem into two subproblems by setting (x + -0.375) equal to 4.597893539 and -4.597893539.Subproblem 1
x + -0.375 = 4.597893539 Simplifying x + -0.375 = 4.597893539 Reorder the terms: -0.375 + x = 4.597893539 Solving -0.375 + x = 4.597893539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 4.597893539 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.597893539 + 0.375 x = 4.597893539 + 0.375 Combine like terms: 4.597893539 + 0.375 = 4.972893539 x = 4.972893539 Simplifying x = 4.972893539Subproblem 2
x + -0.375 = -4.597893539 Simplifying x + -0.375 = -4.597893539 Reorder the terms: -0.375 + x = -4.597893539 Solving -0.375 + x = -4.597893539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -4.597893539 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.597893539 + 0.375 x = -4.597893539 + 0.375 Combine like terms: -4.597893539 + 0.375 = -4.222893539 x = -4.222893539 Simplifying x = -4.222893539Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.972893539, -4.222893539}
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