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Simplifying 4x2 + 21x + -10 = 0 Reorder the terms: -10 + 21x + 4x2 = 0 Solving -10 + 21x + 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'. -2.5 + 5.25x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 5.25x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 5.25x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 5.25x + x2 = 0 + 2.5 5.25x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 5.25x + x2 = 2.5 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 2.5 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 2.5 + 6.890625 Combine like terms: 2.5 + 6.890625 = 9.390625 6.890625 + 5.25x + x2 = 9.390625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (x + 2.625) equal to 3.064412668 and -3.064412668.Subproblem 1
x + 2.625 = 3.064412668 Simplifying x + 2.625 = 3.064412668 Reorder the terms: 2.625 + x = 3.064412668 Solving 2.625 + x = 3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.064412668 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.064412668 + -2.625 x = 3.064412668 + -2.625 Combine like terms: 3.064412668 + -2.625 = 0.439412668 x = 0.439412668 Simplifying x = 0.439412668Subproblem 2
x + 2.625 = -3.064412668 Simplifying x + 2.625 = -3.064412668 Reorder the terms: 2.625 + x = -3.064412668 Solving 2.625 + x = -3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.064412668 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.064412668 + -2.625 x = -3.064412668 + -2.625 Combine like terms: -3.064412668 + -2.625 = -5.689412668 x = -5.689412668 Simplifying x = -5.689412668Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.439412668, -5.689412668}
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