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Simplifying 5x2 + -21 = 12x Reorder the terms: -21 + 5x2 = 12x Solving -21 + 5x2 = 12x Solving for variable 'x'. Reorder the terms: -21 + -12x + 5x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -21 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -2.4x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -2.4x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -2.4x + x2 = 0 + 4.2 -2.4x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -2.4x + x2 = 4.2 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 4.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 4.2 + 1.44 Combine like terms: 4.2 + 1.44 = 5.64 1.44 + -2.4x + x2 = 5.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (x + -1.2) equal to 2.374868417 and -2.374868417.Subproblem 1
x + -1.2 = 2.374868417 Simplifying x + -1.2 = 2.374868417 Reorder the terms: -1.2 + x = 2.374868417 Solving -1.2 + x = 2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.374868417 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.374868417 + 1.2 x = 2.374868417 + 1.2 Combine like terms: 2.374868417 + 1.2 = 3.574868417 x = 3.574868417 Simplifying x = 3.574868417Subproblem 2
x + -1.2 = -2.374868417 Simplifying x + -1.2 = -2.374868417 Reorder the terms: -1.2 + x = -2.374868417 Solving -1.2 + x = -2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.374868417 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.374868417 + 1.2 x = -2.374868417 + 1.2 Combine like terms: -2.374868417 + 1.2 = -1.174868417 x = -1.174868417 Simplifying x = -1.174868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.574868417, -1.174868417}
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